Goodwill and Other Intangible Assets - Intangible Assets, Net - Additional Information (Details) - USD ($)	3 Months Ended	6 Months Ended
Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021
Goodwill And Intangible Assets Disclosure [Abstract]
Impairment of long-lived asset			$ 0
Amortization expense related to intangible assets	$ 4,000,000.0	$ 5,100,000	9,100,000	$ 10,100,000
Expected amortization of intangible assets for remainder of 2022	$ 5,500,000		$ 5,500,000

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
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Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
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Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
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