Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Goodwill [Roll Forward]
Goodwill, beginning	$ 168,284	$ 83,954
Goodwill attributable to preliminary purchase price adjustments and acquisition activity	18,721	84,330
Goodwill reassigned in segment realignment	0
Goodwill, ending	187,005	168,284
Merchant Services
Goodwill [Roll Forward]
Goodwill, beginning	117,334	70,936
Goodwill attributable to preliminary purchase price adjustments and acquisition activity	(933)	46,398
Goodwill reassigned in segment realignment	(419)
Goodwill, ending	115,982	117,334
Accumulated impairment losses			$ 11,458
Proprietary Software and Payments
Goodwill [Roll Forward]
Goodwill, beginning	50,950	13,018
Goodwill attributable to preliminary purchase price adjustments and acquisition activity	19,654	37,932
Goodwill reassigned in segment realignment	419
Goodwill, ending	71,023	50,950
Accumulated impairment losses			0
Other
Goodwill [Roll Forward]
Goodwill, beginning	0	0
Goodwill attributable to preliminary purchase price adjustments and acquisition activity	0	0
Goodwill reassigned in segment realignment	0
Goodwill, ending	$ 0	$ 0
Accumulated impairment losses			$ 0