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Stockholders' Equity - Additional Information (Detail) (USD $) | 0 Months Ended | 3 Months Ended | 12 Months Ended | 1 Months Ended | 7 Months Ended | 0 Months Ended | 9 Months Ended |  |  |  |
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Jul. 02, 2014 | Dec. 31, 2014 | Sep. 30, 2014 | Jun. 30, 2014 | Mar. 31, 2014 | Sep. 30, 2013 | Mar. 31, 2013 Subsidiary | Dec. 31, 2014 | Dec. 31, 2013 | Dec. 31, 2012 | Aug. 31, 2013 | Jul. 31, 2013 | Sep. 30, 2014 | Sep. 29, 2014 | Sep. 30, 2014 | Jul. 30, 2014 | Jun. 28, 2013 | Aug. 02, 2013 | Jan. 31, 2008
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Preferred dividends description |  |  |  |  |  |  |  | Our 4.0% Series A Convertible Preferred Stock ceased accruing daily dividends as a result of redemption in August 2013. Our 4.0% Series B Convertible Preferred Stock ceased accruing daily dividends as a result of the conversion of all of the remaining outstanding shares on September 30, 2014. |  |  |  |  |  |  |  |  |  |  |
Preferred shares outstanding |  | 0 us-gaap_PreferredStockSharesOutstanding |  |  |  |  |  | 0 us-gaap_PreferredStockSharesOutstanding |  |  |  |  |  |  |  |  |  |  |
Preferred dividends accrued |  |  |  |  |  |  |  |  | $ 4,000,000 us-gaap_DividendsPayableCurrent |  |  |  |  |  |  |  |  |  |
Payment for preferred stock redemption |  |  |  |  |  |  |  |  | 474,000,000 us-gaap_PaymentsForRepurchaseOfPreferredStockAndPreferenceStock |  |  |  |  |  |  |  |  |  |
Preferred stock redemption premium |  |  |  |  |  | 232,000,000 us-gaap_PreferredStockRedemptionPremium |  |  | 232,000,000 us-gaap_PreferredStockRedemptionPremium |  |  |  |  |  |  |  |  |  |
Terms of conversion - closing price of common stock | $ 22.24 dan_TermsOfConversionClosingStockPrice |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Terms of conversion - consecutive trading days | 20 days |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Common stock conversion price of preferred shares | $ 11.93 dan_StockConversionPricePerShare |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Conversion Notice Period | 90 days |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Common stock, shares authorized |  | 450,000,000 us-gaap_CommonStockSharesAuthorized |  |  |  |  |  | 450,000,000 us-gaap_CommonStockSharesAuthorized | 450,000,000 us-gaap_CommonStockSharesAuthorized |  |  |  |  |  |  |  |  |  |
Common stock, par value |  | $ 0.01 us-gaap_CommonStockParOrStatedValuePerShare |  |  |  |  |  | $ 0.01 us-gaap_CommonStockParOrStatedValuePerShare | $ 0.01 us-gaap_CommonStockParOrStatedValuePerShare |  |  |  |  |  |  |  |  |  |
Common stock, shares issued |  | 167,659,047 us-gaap_CommonStockSharesIssued |  |  |  |  |  | 167,659,047 us-gaap_CommonStockSharesIssued |  |  |  |  |  |  |  |  |  |  |
Common stock, shares outstanding |  | 166,070,057 us-gaap_CommonStockSharesOutstanding |  |  |  |  |  | 166,070,057 us-gaap_CommonStockSharesOutstanding | 145,338,342 us-gaap_CommonStockSharesOutstanding |  |  |  |  |  |  |  |  |  |
Treasury stock, shares |  | 1,588,990 us-gaap_TreasuryStockShares |  |  |  |  |  | 1,588,990 us-gaap_TreasuryStockShares | 18,742,288 us-gaap_TreasuryStockShares |  |  |  |  |  |  |  |  |  |
Quarterly dividend declared |  | $ 0.05 us-gaap_CommonStockDividendsPerShareDeclared | $ 0.05 us-gaap_CommonStockDividendsPerShareDeclared | $ 0.05 us-gaap_CommonStockDividendsPerShareDeclared | $ 0.05 us-gaap_CommonStockDividendsPerShareDeclared |  |  | $ 0.20 us-gaap_CommonStockDividendsPerShareDeclared | $ 0.20 us-gaap_CommonStockDividendsPerShareDeclared | $ 0.20 us-gaap_CommonStockDividendsPerShareDeclared |  |  |  |  |  |  |  |  |
Dividends declared and paid |  |  |  |  |  |  |  | 32,000,000 dan_DividendsDeclaredAndPaidCommonStockCash |  |  |  |  |  |  |  |  |  |  |
Treasury stock reissued |  |  |  |  |  |  |  | 14,879,935 us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued |  |  |  |  |  |  |  |  |  |  |
Treasury stock reissued, charge to additional paid-in capital |  |  |  |  |  |  |  | 127,000,000 dan_TreasuryStockReissuedAtLowerThanRepurchasePriceOther |  |  |  |  |  |  |  |  |  |  |
Treasury shares retired |  |  |  |  |  |  |  | 14,600,000 us-gaap_TreasuryStockSharesRetired |  |  |  |  |  |  |  |  |  |  |
Treasury stock retired, charge to additional paid-in capital |  |  |  |  |  |  |  | 0 us-gaap_TreasuryStockRetiredCostMethodAmount |  |  |  |  |  |  |  |  |  |  |
Share repurchase program amount |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 1,400,000,000 us-gaap_StockRepurchaseProgramAuthorizedAmount1 | 1,000,000,000 us-gaap_StockRepurchaseProgramAuthorizedAmount1 |  |
Cash spent to repurchase common stock |  |  |  |  |  |  |  | 260,000,000 us-gaap_PaymentsForRepurchaseOfCommonStock | 337,000,000 us-gaap_PaymentsForRepurchaseOfCommonStock | 15,000,000 us-gaap_PaymentsForRepurchaseOfCommonStock |  |  |  |  |  |  |  |  |
Shares repurchased |  |  |  |  |  |  |  | 12,215,451 us-gaap_TreasuryStockSharesAcquired |  |  |  |  |  |  |  |  |  |  |
Available for future share repurchases |  | 311,000,000 us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1 |  |  |  |  |  | 311,000,000 us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1 |  |  |  |  |  |  |  |  |  |  |
Number of subsidiaries in which noncontrolling interests were purchased |  |  |  |  |  |  | 3 dan_NumberOfSubsidiariesInWhichNoncontrollingInterestsWerePurchased |  |  |  |  |  |  |  |  |  |  |  |
Payments to Noncontrolling Interests |  |  |  |  |  |  | 7,000,000 us-gaap_PaymentsToMinorityShareholders |  | 7,000,000 us-gaap_PaymentsToMinorityShareholders |  |  |  |  |  |  |  |  |  |
Series A Preferred Stock [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Preferred shares issued |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 2,500,000.0 us-gaap_PreferredStockSharesIssued / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember
Series A and Series B preferred stock dividend rate percentage |  |  |  |  |  |  |  |  |  |  |  | 4.00%us-gaap_PreferredStockDividendRatePercentage / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember |  |  |  |  |  |  |
Preferred shares outstanding |  | 0 us-gaap_PreferredStockSharesOutstanding / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember |  |  |  |  |  | 0 us-gaap_PreferredStockSharesOutstanding / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember | 0 us-gaap_PreferredStockSharesOutstanding / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember |  |  |  |  |  |  |  |  |  |
Payment for preferred stock redemption |  |  |  |  |  |  |  |  |  |  | 474,000,000 us-gaap_PaymentsForRepurchaseOfPreferredStockAndPreferenceStock / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember |  |  |  |  |  |  |  |
Payment of preferred stock redemption costs |  |  |  |  |  |  |  |  |  |  | 3,000,000 dan_PaymentOfPreferredStockRedemptionCosts / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember |  |  |  |  |  |  |  |
Preferred stock carrying value |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 242,000,000 us-gaap_PreferredStockValue / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember |
Preferred stock redemption premium |  |  |  |  |  |  |  |  |  |  | 232,000,000 us-gaap_PreferredStockRedemptionPremium / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesAPreferredStockMember |  |  |  |  |  |  |  |
Preferred Stock [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Preferred dividends accrued |  |  |  |  |  |  |  |  | 4,000,000 us-gaap_DividendsPayableCurrent / us-gaap_StatementClassOfStockAxis = us-gaap_PreferredStockMember |  |  |  |  |  |  |  |  |  |
Series B Preferred Stock [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Preferred shares issued |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 5,400,000.0 us-gaap_PreferredStockSharesIssued / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember
Series A and Series B preferred stock dividend rate percentage |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 4.00%us-gaap_PreferredStockDividendRatePercentage / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  |
Preferred shares outstanding |  | 0 us-gaap_PreferredStockSharesOutstanding / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  |  |  | 0 us-gaap_PreferredStockSharesOutstanding / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember | 3,803,774 us-gaap_PreferredStockSharesOutstanding / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  |  |  |  |  |  |  |
Shares of preferred stock converted |  |  |  |  |  |  |  | 1,772,693 us-gaap_ConversionOfStockSharesConverted1 / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember | 1,417,425 us-gaap_ConversionOfStockSharesConverted1 / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  | 1,506,972 us-gaap_ConversionOfStockSharesConverted1 / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember | 2,296,802 us-gaap_ConversionOfStockSharesConverted1 / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  |  |
Common shares issued upon conversion |  |  |  |  |  |  |  |  | 11,985,254 us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  | 12,631,780 us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember | 19,517,593 us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  |  |
Total fair value of the conversions |  |  |  |  |  |  |  |  | 249,000,000 dan_SharesSubjectToConversionFairValueOfConversions / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  | 250,000,000 dan_SharesSubjectToConversionFairValueOfConversions / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember | 409,000,000 dan_SharesSubjectToConversionFairValueOfConversions / us-gaap_StatementClassOfStockAxis = us-gaap_SeriesBPreferredStockMember |  |  |  |  |
Additional Paid-in Capital [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock retired, charge to additional paid-in capital |  |  |  |  |  |  |  | $ (294,000,000)us-gaap_TreasuryStockRetiredCostMethodAmount / us-gaap_StatementEquityComponentsAxis = us-gaap_AdditionalPaidInCapitalMember |  |  |  |  |  |  |  |  |  |  |

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