Summary of Significant Accounting Policies (Details) - USD ($)	3 Months Ended		9 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Mar. 31, 2021	Sep. 30, 2020
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Selling and administrative expenses	$ 215,900,000	$ 202,300,000	$ 648,600,000
Acquisition-related intangible asset amortization			80,700,000	$ 81,300,000
Selling and administrative expense, revised				609,000,000.0
Cares Act	21,700,000		21,700,000
Accumulated Other Comprehensive Income (Loss), Foreign Currency Translation Adjustment, Net of Tax	100,000		200,000
Standard Product Warranty Accrual, Increase for Warranties Issued	5,800,000		16,900,000
Standard Product Warranty Accrual, Decrease for Payments	(6,000,000.0)		(17,700,000)
Retained Earnings (Accumulated Deficit)	2,278,400,000		2,278,400,000			$ 2,132,200,000
Standard Product Warranty Accrual	30,200,000		30,200,000		$ 30,300,000	$ 30,800,000
Non-cash Investing Activities			17,300,000	$ 3,900,000
Accounting Standards Update 2016-13 [Member]
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Deferred Tax Assets, Valuation Allowance	800,000		800,000
Retained Earnings (Accumulated Deficit)	3,000,000.0		3,000,000.0
Accounting Standards Update 2016-13 [Member] | Cumulative Effect, Period of Adoption, Adjustment [Member]
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Retained Earnings (Accumulated Deficit)	$ 2,200,000		$ 2,200,000