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Subsequent Events - Additional Information (Detail) - Subsequent Event [Member] - Common Stock [Member] $ in Billions	Feb. 04, 2025 USD ($)
Subsequent Event [Line Items]
Share authorization date	Feb. 04, 2025
Number of shares authorized to be repurchased	$ 1
Effective Date of existing authorization of shares	Feb. 04, 2025
Expiration Date of existing authorization of shares	Jan. 29, 2026

X

- Definition

Share repurchase program authorized date.

+ References

No definition available.

+ Details

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Namespace Prefix:	fbin_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Stock repurchase program effective date.

+ References

No definition available.

+ Details

Name:	fbin_StockRepurchaseProgramEffectiveDate
Namespace Prefix:	fbin_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount authorized for purchase of share under share repurchase plan. Includes, but is not limited to, repurchase of stock and unit of ownership.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481520/505-30-50-4

+ Details

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Namespace Prefix:	srt_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Expiration date for purchase of share under share repurchase plan, in YYYY-MM-DD format. Includes, but is not limited to, repurchase of stock and unit of ownership.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481520/505-30-50-4

+ Details

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Namespace Prefix:	srt_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Detail information of subsequent event by type. User is expected to use existing line items from elsewhere in the taxonomy as the primary line items for this disclosure, which is further associated with dimension and member elements pertaining to a subsequent event.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 830
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481674/830-30-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 855
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483399/855-10-50-2

+ Details

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Balance Type:	na
Period Type:	duration

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: