CONDENSED FINANCIAL INFORMATION OF REGISTRANT (PARENT COMPANY ONLY) - Schedule of Balance Sheets (Detail) - USD ($)	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Non-current assets:
Total assets	$ 2,167,711,000	$ 2,343,876,000	$ 2,371,627,000
LIABILITIES AND STOCKHOLDERS’ EQUITY:
Total liabilities	810,846,000	933,563,000
Stockholders’ equity:
Preferred stock, $0.001 par value; 1,000,000 shares authorized and no shares issued and outstanding at September 30, 2024 and September 30, 2023, respectively	0	0
Additional paid-in capital	1,694,066,000	1,662,322,000
Retained earnings (accumulated deficit)	89,002,000	(64,377,000)
Accumulated other comprehensive income (loss)	(1,682,000)	1,878,000
Treasury stock, at cost, 14,134,558 shares at September 30, 2024 and 8,268,423 shares at September 30, 2023	(424,678,000)	(189,666,000)
Total stockholders’ equity	1,356,865,000	1,410,313,000	$ 1,430,707,000	$ 1,421,495,000
Total liabilities and stockholders’ equity	$ 2,167,711,000	$ 2,343,876,000
Preferred stock, par value per share (in dollars per share)	$ 0.001	$ 0.001
Preferred stock, shares authorized (in shares)	1,000,000	1,000,000
Preferred stock, shares outstanding (in shares)	0	0
Preferred stock, shares issued (in shares)	0	0
Treasury stock, shares (in shares)	14,134,558	8,268,423
Parent Company
Non-current assets:
Investments in subsidiaries	$ 1,356,865,000	$ 1,410,313,000
Total non-current assets	1,356,865,000	1,410,313,000
Total assets	1,356,865,000	1,410,313,000
LIABILITIES AND STOCKHOLDERS’ EQUITY:
Total liabilities	0	0
Stockholders’ equity:
Preferred stock, $0.001 par value; 1,000,000 shares authorized and no shares issued and outstanding at September 30, 2024 and September 30, 2023, respectively	0	0
Additional paid-in capital	1,694,066,000	1,662,322,000
Retained earnings (accumulated deficit)	89,002,000	(64,377,000)
Accumulated other comprehensive income (loss)	(1,682,000)	1,878,000
Treasury stock, at cost, 14,134,558 shares at September 30, 2024 and 8,268,423 shares at September 30, 2023	(424,678,000)	(189,666,000)
Total stockholders’ equity	1,356,865,000	1,410,313,000
Total liabilities and stockholders’ equity	$ 1,356,865,000	$ 1,410,313,000
Preferred stock, par value per share (in dollars per share)	$ 0.001	$ 0.001
Preferred stock, shares authorized (in shares)	1,000,000	1,000,000
Preferred stock, shares outstanding (in shares)	0	0
Preferred stock, shares issued (in shares)	0	0
Treasury stock, shares (in shares)	14,134,558	8,268,423
Class A
Stockholders’ equity:
Common stock value	$ 157,000	$ 156,000
Common stock, par value per share (in dollars per share)	$ 0.001	$ 0.001
Common stock, shares authorized (in shares)	1,100,000,000	1,100,000,000
Common stock, shares issued (in shares)	157,148,821	155,967,736
Common stock, shares outstanding (in shares)	143,014,263
Class A | Parent Company
Stockholders’ equity:
Common stock value	$ 157,000	$ 156,000
Common stock, par value per share (in dollars per share)	$ 0.001	$ 0.001
Common stock, shares authorized (in shares)	1,100,000,000	1,100,000,000
Common stock, shares issued (in shares)	157,148,821	155,967,736
Class B
Stockholders’ equity:
Common stock value	$ 0	$ 0
Common stock, par value per share (in dollars per share)	$ 0.001	$ 0.001
Common stock, shares authorized (in shares)	100,000,000	100,000,000
Common stock, shares issued (in shares)	0	100
Common stock, shares outstanding (in shares)	0	100
Class B | Parent Company
Stockholders’ equity:
Common stock value	$ 0	$ 0
Common stock, par value per share (in dollars per share)	$ 0.001	$ 0.001
Common stock, shares authorized (in shares)	100,000,000	100,000,000
Common stock, shares issued (in shares)	0	100
Common stock, shares outstanding (in shares)	0	100