Segment Information - Summary of Segment Information (Details)	12 Months Ended
	Sep. 30, 2022 USD ($) Segment	Sep. 30, 2021 USD ($)	Sep. 30, 2020 USD ($)
Segment Reporting [Abstract]
Number of reportable segments | Segment	2
Segment revenues:
Revenue	$ 1,377,270,000	$ 1,316,536,000	$ 1,294,562,000
Segment operating expense	(834,856,000)	(811,047,000)	(998,593,000)
Operating income	542,414,000	505,489,000	295,969,000
Unallocated share-based compensation expense	(115,355,000)	(112,457,000)	(93,681,000)
Unallocated amortization expense	(2,061,000)	(3,255,000)	(4,993,000)
Unallocated restructuring and impairment charges	0	(7,957,000)	(45,029,000)
Unallocated interest expense, net	(68,967,000)	(40,092,000)	(42,177,000)
Unallocated other income (expense), net	(2,138,000)	7,745,000	3,208,000
Depreciation expense	15,242,000	20,319,000	23,453,000
Gain (Loss) on Disposition of Business	0	100,139,000	0
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest	471,309,000	473,142,000	257,000,000
Software
Segment revenues:
Revenue	670,627,000	662,389,000	766,015,000
Scores
Segment revenues:
Revenue	706,643,000	654,147,000	528,547,000
Operating Segments
Segment revenues:
Revenue	1,377,270,000	1,316,536,000	1,294,562,000
Segment operating expense	(717,440,000)	(787,517,000)	(854,890,000)
Operating income	659,830,000	529,019,000	439,672,000
Operating Segments | Software
Segment revenues:
Revenue	670,627,000	662,389,000	766,015,000
Segment operating expense	(485,175,000)	(557,242,000)	(635,949,000)
Operating income	185,452,000	105,147,000	130,066,000
Depreciation expense	14,412,000	19,505,000	22,418,000
Operating Segments | Scores
Segment revenues:
Revenue	706,643,000	654,147,000	528,547,000
Segment operating expense	(83,837,000)	(93,463,000)	(74,237,000)
Operating income	622,806,000	560,684,000	454,310,000
Depreciation expense	723,000	667,000	617,000
Unallocated Corporate Expenses
Segment revenues:
Segment operating expense	(148,428,000)	(136,812,000)	(144,704,000)
Operating income	(148,428,000)	(136,812,000)	(144,704,000)
Depreciation expense	107,000	147,000	418,000
On-premises and SaaS software
Segment revenues:
Revenue	564,751,000	517,888,000	584,576,000
On-premises and SaaS software | Operating Segments
Segment revenues:
Revenue	564,751,000	517,888,000	584,576,000
On-premises and SaaS software | Operating Segments | Software
Segment revenues:
Revenue	564,751,000	517,888,000	584,576,000
On-premises and SaaS software | Operating Segments | Scores
Segment revenues:
Revenue	0	0	0
Professional services
Segment revenues:
Revenue	105,876,000	144,501,000	181,439,000
Professional services | Operating Segments
Segment revenues:
Revenue	105,876,000	144,501,000	181,439,000
Professional services | Operating Segments | Software
Segment revenues:
Revenue	105,876,000	144,501,000	181,439,000
Professional services | Operating Segments | Scores
Segment revenues:
Revenue	0	0	0
Scores Products
Segment revenues:
Revenue	706,643,000	654,147,000	528,547,000
Scores Products | Operating Segments
Segment revenues:
Revenue	706,643,000	654,147,000	528,547,000
Scores Products | Operating Segments | Software
Segment revenues:
Revenue	0	0	0
Scores Products | Operating Segments | Scores
Segment revenues:
Revenue	$ 706,643,000	$ 654,147,000	$ 528,547,000