Income Taxes (Schedule of Effective Income Tax Rate Reconciliation) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Effective Income Tax Rate Reconciliation, Amount [Abstract]
Computed tax at federal statutory rate	$ (64.2)	$ 32.4	$ 14.2
State income taxes, net of federal tax benefit	(9.7)	0.2	(0.7)
Foreign rate differential	4.4	0.8	2.0
Other taxes including repatriation of foreign earnings and GILTI	2.4	5.5	4.4
Foreign tax incentives	(2.8)	(3.7)	(3.6)
Uncertain tax positions	(10.1)	0.2	2.1
Nondeductible transaction expenses	0.0	0.0	1.0
Debt refinancing	0.0	(3.4)	0.0
Tax structuring	0.0	(39.5)	0.0
Other, net	6.0	0.8	1.5
(Benefit)/provision for income taxes	$ (74.0)	$ (6.7)	$ 20.9
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Computed tax at federal statutory rate, percent	21.00%	21.00%	21.00%
State income taxes, net of federal tax benefit, percent	3.20%	0.10%	(1.00%)
Foreign tax less than the federal rate, percent	(1.40%)	0.50%	3.00%
Other taxes including repatriation of foreign earnings, percent	(0.80%)	3.60%	6.50%
Foreign tax incentives, period	0.90%	(2.40%)	(5.30%)
Uncertain tax positions	3.30%	0.10%	3.10%
Nondeductible transaction expenses, percent	0.00%	0.00%	1.50%
Debt refinancing	0	(0.022)	0
Tax structuring	0	(0.256)	0
Other, net, percent	(2.00%)	0.60%	2.10%
Effective Income Tax Rate Reconciliation, Percent	24.20%	(4.30%)	30.90%