Segment Reporting (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Segment Reporting Information [Line Items]
Rental revenues	$ 116,491	$ 113,933	$ 105,939
Total revenues	909,402	896,167	689,268
Gross profit (loss), by segment	114,785	121,923	(108,562)
Interest expense	67,600	71,500	75,900
Depreciation and amortization	37,952	39,885	42,829
Goodwill and intangible assets, closure and other impairment charges	3,100	5,400	132,600
Capital expenditures	35,318	16,849	10,927
Goodwill	253,956	251,628	251,600	$ 343,800
Total assets	1,881,491	1,999,366	2,074,900
Operating Segments
Segment Reporting Information [Line Items]
Gross profit (loss), by segment	377,300	375,200	248,700
Goodwill	254,000	251,600	251,600
Corporate
Segment Reporting Information [Line Items]
Gross profit (loss), by segment	(262,600)	(253,300)	(357,300)
Interest expense	60,700	63,300	66,900
Depreciation and amortization	13,000	11,700	13,400
Capital expenditures	31,000	10,300	8,200
Total assets	332,800	424,900	454,700
Franchise operations
Segment Reporting Information [Line Items]
Revenue from contract with customer	662,438	631,936	469,453
Company restaurants
Segment Reporting Information [Line Items]
Revenue from contract with customer	126,869	146,000	108,054
Financing operations
Segment Reporting Information [Line Items]
Revenue from contract with customer	3,604	4,298	5,822
Franchise operations | Operating Segments
Segment Reporting Information [Line Items]
Gross profit (loss), by segment	340,500	336,000	230,500
Depreciation and amortization	10,000	10,100	10,100
Goodwill and intangible assets, closure and other impairment charges	3,100	1,700	122,100
Total assets	1,123,000	991,000	997,700
Franchise operations | Franchise operations | Operating Segments
Segment Reporting Information [Line Items]
Revenue from contract with customer	662,400	631,900	469,500
Goodwill	254,000	247,000	247,000
Rental operations | Operating Segments
Segment Reporting Information [Line Items]
Rental revenues	116,500	113,900	105,900
Gross profit (loss), by segment	28,500	26,100	16,400
Interest expense	4,300	4,900	6,300
Depreciation and amortization	10,700	11,100	12,300
Total assets	390,600	426,600	451,500
Company restaurants | Operating Segments
Segment Reporting Information [Line Items]
Gross profit (loss), by segment	5,100	9,300	(3,500)
Interest expense	2,600	3,300	2,700
Depreciation and amortization	4,300	7,000	7,000
Goodwill and intangible assets, closure and other impairment charges	0	3,700	10,500
Capital expenditures	4,300	6,500	2,700
Total assets	3,300	117,200	121,100
Company restaurants | Company restaurants
Segment Reporting Information [Line Items]
Revenue from contract with customer	126,900	146,000
Company restaurants | Company restaurants | Operating Segments
Segment Reporting Information [Line Items]
Revenue from contract with customer			108,100
Goodwill	0	4,600	4,600
Financing operations | Operating Segments
Segment Reporting Information [Line Items]
Gross profit (loss), by segment	3,200	3,800	5,300
Total assets	31,800	39,700	49,900
Financing operations | Financing operations | Operating Segments
Segment Reporting Information [Line Items]
Revenue from contract with customer	$ 3,600	$ 4,300	$ 5,800