Stockholders' Equity - Schedule of Reclassifications From Accumulated Other Comprehensive Income (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Accumulated Other Comprehensive Income (Loss) [Line Items]
Amortization of pension and other postretirement plan prior service credits	$ 11.7	$ (27.6)	$ 6.9
Business disposal	3.0	(1,220.3)	(314.9)
Income tax expense (benefit)	69.1	37.1	34.7
Discontinued Operations, Held-for-sale
Accumulated Other Comprehensive Income (Loss) [Line Items]
Business disposal	3.0	(1,220.3)	(314.9)
Income tax expense (benefit)	(11.1)	432.6	(33.5)
Currency translation adjustment loss	4.4	30.7
Net periodic benefit loss (income)		(0.1)
Reclassification out of Accumulated Other Comprehensive Income
Accumulated Other Comprehensive Income (Loss) [Line Items]
Amortization of pension and other postretirement plan prior service credits	(2.1)	(2.1)	(2.1)
Business disposal	4.4	30.6	0.0
Loss (gain) on cash flow hedges	2.3	12.7	1.4
Income tax expense (benefit)	2.5	3.0	(3.4)
Other comprehensive income (loss), net of tax	$ 7.1	$ 44.2	$ (4.1)