Segment Information (Details) $ in Thousands	12 Months Ended
	Sep. 30, 2024 USD ($) region state segment	Sep. 30, 2023 USD ($)	Sep. 30, 2022 USD ($)	May 19, 2022
Segment Reporting [Abstract]
Number of states with active operations | state	13
Number of regions in which entity operates | region	3
Number of reportable segments | segment	3
Segment Reporting Information [Line Items]
Total revenue	$ 2,330,197	$ 2,206,785	$ 2,316,988
Total operating income	143,026	177,253	272,491
Depreciation and amortization	14,867	12,198	13,360
Capital expenditures	22,353	20,334	15,048
Assets	2,591,527	2,411,033
Gain on sale of investment	8,591	0	0
Imagine Homes
Segment Reporting Information [Line Items]
Equity method investment, ownership percentage				33.00%
Operating Segments
Segment Reporting Information [Line Items]
Total operating income	288,303	328,197	424,833
Depreciation and amortization	13,090	10,867	11,670
Corporate and unallocated
Segment Reporting Information [Line Items]
Total operating income	(145,277)	(150,944)	(152,342)
Depreciation and amortization	1,777	1,331	1,690
Capital expenditures	6,312	6,395	4,870
Assets	633,764	739,986
West
Segment Reporting Information [Line Items]
Total revenue	1,467,287	1,297,005	1,331,553
West | Operating Segments
Segment Reporting Information [Line Items]
Total operating income	189,739	205,850	253,961
Depreciation and amortization	9,820	7,550	8,178
Capital expenditures	11,956	9,909	7,755
Assets	1,114,450	994,597
East
Segment Reporting Information [Line Items]
Total revenue	501,206	505,844	560,747
East | Operating Segments
Segment Reporting Information [Line Items]
Total operating income	52,898	65,021	102,146
Depreciation and amortization	1,792	1,662	1,649
Capital expenditures	2,559	2,578	1,208
Assets	454,255	356,020
Southeast
Segment Reporting Information [Line Items]
Total revenue	361,704	403,936	424,688
Southeast | Operating Segments
Segment Reporting Information [Line Items]
Total operating income	45,666	57,326	68,726
Depreciation and amortization	1,478	1,655	1,843
Capital expenditures	1,526	1,452	$ 1,215
Assets	$ 389,058	$ 320,430