INCOME TAXES - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Income Taxes [Line Items]
Gross increase – tax positions in prior period	$ 77.5	$ 21.5	$ 84.4
Income tax credits and adjustments			3.2
Mandatory repatriation tax payable period	8 years
Repatriation tax liability	$ 11.1
Repatriation tax liability due and payable in the next 12 months, will be offset	5.2
Taxes on unremitted foreign earnings	1.7	1.2
Undistributed foreign earnings were taxed in the U.S.	500.6
Tax reform act, income tax expense (benefit)	23.9
Undistributed foreign earnings, high-tax exceptions	53.5
Undistributed foreign earnings, taxed	183.1
Operating loss carryforwards, domestic	119.5
U.S. state net operating loss carryforwards	42.8
Operating loss carryforwards, foreign	114.6
Deferred tax assets, valuation allowance	321.4	333.4	337.4
Increase (decrease) in valuation allowance, deferred tax asset	(12.0)	(4.0)
Unrecognized tax benefits	190.2	121.1	100.9	$ 18.0
Unrecognized tax benefits that would impact effective tax rate	102.1
Unrecognized tax benefits, income tax penalties and interest accrued	9.8	1.7
Increase (decrease) in unrecognized tax benefits, income tax penalties and interest expense	8.1	0.3	0.1
Unrecognized tax benefits, decrease resulting from prior period tax positions	9.2	34.4	2.9
Unrecognized tax benefits, increase resulting from current period tax positions	1.7	33.4	1.7
Tax Year 2019
Income Taxes [Line Items]
Gross increase – tax positions in prior period			67.3
Unrecognized tax benefits, decrease resulting from prior period tax positions		33.0
Unrecognized tax benefits, decrease resulting from current period tax positions	2.3
Unrecognized tax benefits, decrease resulting from settlements with taxing authorities	17.9
Federal Net Operating Losses
Income Taxes [Line Items]
U.S. federal operating loss carryforwards expected to expire unused	561.2
Tax benefit related to NOLs expire unused	117.8
U.S. State Net Operating Losses
Income Taxes [Line Items]
Tax benefit related to NOLs expire unused	13.8
Deferred tax assets, valuation allowance	42.3
Foreign Net Operating Losses
Income Taxes [Line Items]
Tax benefit related to NOLs expire unused	112.4
U.S. Net Deferred Tax Assets
Income Taxes [Line Items]
Deferred tax assets, valuation allowance	203.6	244.7	257.5
Increase (decrease) in valuation allowance, deferred tax asset	(41.1)	(12.8)
Foreign Net Deferred Tax Assets
Income Taxes [Line Items]
Deferred tax assets, valuation allowance	117.8	88.7	$ 79.9
Increase (decrease) in valuation allowance, deferred tax asset	29.1	8.8
HHI Segment
Income Taxes [Line Items]
Unrecognized tax benefits, increase resulting from current period tax positions	50.1	27.3
Domestic Tax Jurisdiction
Income Taxes [Line Items]
Operating loss carryforwards	569.2
Foreign Tax Jurisdiction
Income Taxes [Line Items]
Operating loss carryforwards	$ 458.7
June 2019 Regulations
Income Taxes [Line Items]
Gross increase – tax positions in prior period		$ 59.0