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Schedule II - Condensed Financial Information of Registrant - Condensed Statements of Operations of Registrant (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
Sep. 30, 2017
Jun. 30, 2017
Mar. 31, 2017
Dec. 31, 2016
Sep. 30, 2016
Jun. 30, 2016
Mar. 31, 2016
Dec. 31, 2015
Sep. 30, 2017
Sep. 30, 2016
Sep. 30, 2015
Condensed Income Statements, Captions [Line Items]                      
Stockholders' Equity Attributable to Parent $ 758.0       $ 638.1       $ 758.0 $ 638.1  
Consolidated segment revenues                 5,008.5 5,048.6 $ 4,753.8
Gross profit 496.3 $ 473.3 $ 455.2 $ 450.0 485.7 $ 530.7 $ 462.8 $ 440.7      
Operating expenses:                      
Operating income                 516.3 573.5 179.1
Other income (expense):                      
Interest Expense                 (360.1) (402.5) (407.8)
Gain On Contingent Purchase Price Adjustment                     8.5
Other (expense) income, net                 (5.0) 4.8 10.1
Income (loss) from continuing operations before income taxes                 151.2 175.8 (180.1)
Income tax expense                 48.3 31.6 39.6
Net income (loss) from continuing operations 24.0 39.8 (51.4) 260.8 36.2 (93.0) 15.9 7.0 273.2 (33.9) (512.4)
Net income (loss) attributable to common and participating preferred stockholders                 106.0 (198.8) (556.8)
Income (Loss) from Discontinued Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest (25.1) 7.7 (62.7) 250.4 44.5 (185.5) (19.9) (17.2) 170.3 (178.1) (292.7)
Net Income (Loss) Attributable to Parent (26.2) $ 2.1 $ (82.1) $ 212.2 (7.3) $ (132.9) $ (24.7) $ (33.9) 106.0 (198.8) (556.8)
HGI                      
Condensed Income Statements, Captions [Line Items]                      
Consolidated segment revenues                 0.0 0.0 0.0
Cost of revenues                 0.0 0.0 0.0
Gross profit                 0.0 0.0 0.0
Operating expenses:                      
General and administrative                 40.4 50.7 100.2
Acquisition related charges                 0.0 0.2 0.4
Total operating expenses                 40.4 50.9 100.6
Operating income                 (40.4) (50.9) (100.6)
Other income (expense):                      
Equity in net income (losses) of subsidiaries                 497.8 (214.8) (357.2)
Interest Expense                 (144.1) (143.1) (124.2)
Gain On Contingent Purchase Price Adjustment                 0.0 0.0 8.5
Other (expense) income, net                 1.3 2.0 15.2
Income (loss) from continuing operations before income taxes                 314.6 (406.8) (558.3)
Income tax expense                 208.6 (208.0) (1.5)
Net income (loss) from continuing operations                 106.0 (198.8) (556.8)
Discontinued Operations, Held-for-sale [Member]                      
Condensed Income Statements, Captions [Line Items]                      
Stockholders' Equity Attributable to Parent $ 1,536.3       $ 1,351.6       1,536.3 1,351.6  
Consolidated segment revenues                 0.0 0.0  
Operating expenses:                      
Operating income                 0.0 0.0  
Other income (expense):                      
Net income (loss) from continuing operations                 170.3 (178.1)  
Income (Loss) from Discontinued Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest                 170.3 (178.1)  
Discontinued Operations, Held-for-sale [Member] | HGI                      
Condensed Income Statements, Captions [Line Items]                      
Consolidated segment revenues                     0.0
Operating expenses:                      
Operating income                     0.0
Other income (expense):                      
Interest Expense                     0.0
Other (expense) income, net                     0.0
Income (loss) from continuing operations before income taxes                     0.0
Income tax expense                     0.0
Net income (loss) from continuing operations                     (292.7)
Income (Loss) from Discontinued Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest                     (292.7)
Net Income (Loss) Attributable to Parent                 $ 126.6 $ (197.2) $ (314.7)