Summary of Significant Accounting Policies - Additional Information (Details)	12 Months Ended
	Sep. 30, 2020 USD ($) Step	Sep. 30, 2019 USD ($)	Sep. 30, 2018 USD ($)
Accounting Policies [Abstract]
Research and development costs charged to expense	$ 103,900,000	$ 99,000,000.0	$ 99,300,000
Advertising cost	16,000,000.0	24,900,000	21,100,000
Amortization of Debt Issuance Costs	3,600,000	$ 1,600,000	5,600,000
Write off of Deferred Debt Issuance Cost	$ 1,800,000		$ 3,200,000
Number of steps to evaluate uncertain income tax positions (in steps) | Step	2
Minimum percentage likelihood of tax benefit being realized (as a percent)	50.00%
Maximum percentage likelihood of tax benefit being realized (as a percent)	50.00%
Amount of tax benefit realized for tax positions currently estimated to have a less than likelihood percentage of being sustained	$ 0
Maximum remaining maturity period at time of purchase of liquid investments classified as cash equivalents (in months)	3 months
Inventory valued using LIFO method (as a percent)	83.00%	84.00%