Goodwill and Intangible Assets - Net - Summary of Finite-Lived Intangible Assets (Detail) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 670,886	$ 665,786
Accumulated Amortization	(378,512)	(323,368)
Total	$ 292,374	342,418
Minimum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	3 years
Maximum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	20 years
Propriety knowledge [Member]
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 289,300	289,300
Accumulated Amortization	(195,303)	(171,686)
Total	$ 93,997	$ 117,614
Propriety knowledge [Member] | Minimum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	10 years	10 years
Propriety knowledge [Member] | Maximum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	15 years	15 years
Trademarks [Member]
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 223,840	$ 223,140
Accumulated Amortization	(124,521)	(108,096)
Total	$ 99,319	$ 115,044
Trademarks [Member] | Minimum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	5 years	5 years
Trademarks [Member] | Maximum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	20 years	20 years
Customer relationships [Member]
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 146,670	$ 142,270
Accumulated Amortization	(52,119)	(39,084)
Total	$ 94,551	$ 103,186
Customer relationships [Member] | Minimum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	15 years	15 years
Customer relationships [Member] | Maximum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	19 years	19 years
Patents [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	10 years	10 years
Gross Carrying Value	$ 7,000	$ 7,000
Accumulated Amortization	(3,182)	(2,132)
Total	3,818	4,868
Other intangible [Member]
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Value	4,076	4,076
Accumulated Amortization	(3,387)	(2,370)
Total	$ 689	$ 1,706
Other intangible [Member] | Minimum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	3 years	3 years
Other intangible [Member] | Maximum [Member]
Finite-Lived Intangible Assets [Line Items]
Lives in Years	15 years	15 years