SEGMENT INFORMATION - Schedule of Segment Information (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Apr. 02, 2023	Mar. 31, 2024	Apr. 02, 2023	Apr. 03, 2022
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total segment adjusted EBITDA	$ 109.3	$ 59.5	$ 188.1	$ 107.6
Corporate	(3.0)	8.5	(8.5)	16.8
Interest expense	16.9	31.6	36.1	65.0
Depreciation	14.3	11.9	28.8	24.1
Amortization	11.1	10.5	22.2	20.9
Share based compensation	4.5	4.5	8.4	7.7
HPC separation initiatives	2.8	1.1	3.1	3.5
Fiscal 2023 and 2022 restructuring	0.4	4.6	0.9	5.1
Global ERP transformation	3.9	3.3	6.9	4.9
Russia closing initiative	0.0	(0.1)	0.0	2.8
Non-cash purchase accounting adjustments	0.5	0.5	0.9	0.9
Impairment of equipment and operating lease assets	0.5	4.2	0.5	4.5
Impairment of intangible assets	39.0	67.0	43.0	67.0
Representation and warranty insurance proceeds	(65.0)	0.0	(65.0)	0.0	$ 0.0
Legal and environmental	0.3	0.0	1.5		0.0
Gain from debt repurchase	0.0	0.0	(4.7)	0.0
Unallocated shared costs	0.0	6.3	0.0	12.5
Early settlement of foreign currency cash flow hedges	0.0	1.3	0.0	3.9
Gain from remeasurement of contingent consideration liability	0.0	0.0	0.0	(1.5)
Other	0.1	0.6	0.5	5.0
Income (loss) from continuing operations before income taxes	75.4	(109.8)	105.3	(161.9)
HHI divestiture and separation costs
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Transaction related charges	0.8	1.4	2.1	2.9
Tristar integration
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Transaction related charges	0.0	4.0	0.0	9.7
Other project costs
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Transaction related charges	0.1	6.5	0.1	11.9
GPC
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total segment adjusted EBITDA	62.3	46.3	115.1	83.5
H&G
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total segment adjusted EBITDA	29.2	15.1	28.5	12.8
HPC
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total segment adjusted EBITDA	17.8	(1.9)	44.5	11.3
HPC product recall	6.7	1.6	6.0	1.9
SB/RH
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total segment adjusted EBITDA	109.3	59.5	188.1	107.6
Corporate	(3.2)	8.3	(9.0)	16.7
Interest expense	16.9	31.7	36.1	65.1
Depreciation	14.3	11.9	28.8	24.1
Amortization	11.1	10.5	22.2	20.9
Share based compensation	4.1	4.0	7.8	7.1
HPC separation initiatives	2.8	1.1	3.1	3.5
Fiscal 2023 and 2022 restructuring	0.4	4.6	0.9	5.1
Global ERP transformation	3.9	3.3	6.9	4.9
Russia closing initiative	0.0	(0.1)	0.0	2.8
Non-cash purchase accounting adjustments	0.5	0.5	0.9	0.9
Impairment of equipment and operating lease assets	0.5	4.2	0.5	4.5
Impairment of intangible assets	39.0	67.0	43.0	67.0
Representation and warranty insurance proceeds	(65.0)	0.0	(65.0)	0.0	0.0
Legal and environmental	0.3	0.0	1.5		$ 0.0
Gain from debt repurchase	0.0	0.0	(4.7)	0.0
Unallocated shared costs	0.0	6.3	0.0	12.5
Early settlement of foreign currency cash flow hedges	0.0	1.3	0.0	3.9
Gain from remeasurement of contingent consideration liability	0.0	0.0	0.0	(1.5)
Other	0.1	0.6	0.6	5.0
Income (loss) from continuing operations before income taxes	76.0	(109.2)	106.3	(161.3)
SB/RH | HHI divestiture and separation costs
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Transaction related charges	0.8	1.4	2.1	2.9
SB/RH | Tristar integration
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Transaction related charges	0.0	4.0	0.0	9.7
SB/RH | Other project costs
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Transaction related charges	0.1	6.5	0.1	11.9
SB/RH | GPC
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total segment adjusted EBITDA	62.3	46.3	115.1	83.5
SB/RH | H&G
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total segment adjusted EBITDA	29.2	15.1	28.5	12.8
SB/RH | HPC
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total segment adjusted EBITDA	17.8	(1.9)	44.5	11.3
HPC product recall	$ 6.7	$ 1.6	$ 6.0	$ 1.9