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Segment Information - Financial Information Concerning Reportable Segments (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Jun. 30, 2026
Jun. 30, 2025
Jun. 30, 2026
Jun. 30, 2025
Dec. 31, 2025
Segment Reporting [Line Items]          
Total revenues $ 102.2 $ 110.2 $ 198.4 $ 213.4  
Cost of revenue 85.3 90.8 169.2 181.8  
Interest expense 1.2 3.3 3.5 7.1  
Equity in (loss) earnings of unconsolidated affiliates 1.8 (95.7) (4.0) (97.6)  
Net (loss) earnings from continuing operations 28.4 (229.5) (7.4) (268.2)  
Assets 1,258.4 1,785.8 1,258.4 1,785.8 $ 1,308.9
Goodwill 21.3 53.4 21.3 53.4 $ 53.4
Restaurant Group          
Segment Reporting [Line Items]          
Total revenues 92.0 101.9 183.9 201.0  
Operating Segments | Total Reportable Segments          
Segment Reporting [Line Items]          
Total revenues 92.0 101.9 183.9 201.0  
Cost of revenue 85.3 90.8 169.2 181.8  
Depreciation and amortization 1.7 2.5 3.7 4.9  
Other segment items 52.3 10.4 69.7 19.6  
Interest expense 1.9 1.6 3.7 3.1  
Equity in (loss) earnings of unconsolidated affiliates 10.1 (93.6) 4.0 (103.5)  
Net (loss) earnings from continuing operations (39.1) (97.0) (58.4) (111.9)  
Assets 550.5 652.9 550.5 652.9  
Goodwill 21.3 53.4 21.3 53.4  
Operating Segments | Restaurant Group          
Segment Reporting [Line Items]          
Total revenues 92.0 101.9 183.9 201.0  
Cost of revenue 85.3 90.8 169.2 181.8  
Depreciation and amortization 1.7 2.5 3.7 4.9  
Other segment items 52.3 10.4 69.7 19.6  
Interest expense 1.9 1.6 3.7 3.1  
Equity in (loss) earnings of unconsolidated affiliates 0.0 0.0 0.0 0.0  
Net (loss) earnings from continuing operations (49.2) (3.4) (62.4) (8.4)  
Assets 179.3 260.9 179.3 260.9  
Goodwill 21.3 53.4 21.3 53.4  
Operating Segments | Alight          
Segment Reporting [Line Items]          
Equity in (loss) earnings of unconsolidated affiliates (0.8) (81.7) (2.9) (83.6)  
Net (loss) earnings from continuing operations (0.8) (81.7) (2.9) (83.6)  
Assets 71.1 229.1 71.1 229.1  
Operating Segments | BKFC          
Segment Reporting [Line Items]          
Equity in (loss) earnings of unconsolidated affiliates 10.5 (12.3) 6.1 (22.7)  
Net (loss) earnings from continuing operations 10.5 (12.3) 6.1 (22.7)  
Assets 160.2 106.0 160.2 106.0  
Operating Segments | JANA          
Segment Reporting [Line Items]          
Equity in (loss) earnings of unconsolidated affiliates 0.4 0.4 0.8 2.8  
Net (loss) earnings from continuing operations 0.4 0.4 0.8 2.8  
Assets 139.9 56.9 139.9 56.9  
Operating Segments | Corporate and Other          
Segment Reporting [Line Items]          
Total revenues 10.2 8.3 14.5 12.4  
Net (loss) earnings from continuing operations 67.5 (132.5) 51.0 (156.3)  
Assets 707.9 1,132.9 707.9 1,132.9  
Goodwill 0.0 0.0 0.0 0.0  
Restaurant revenue          
Segment Reporting [Line Items]          
Total revenues 92.0 101.9 183.9 201.0  
Restaurant revenue | Restaurant Group          
Segment Reporting [Line Items]          
Total revenues 92.0 101.9 183.9 201.0  
Restaurant revenue | Operating Segments | Total Reportable Segments          
Segment Reporting [Line Items]          
Total revenues 92.0 101.9 183.9 201.0  
Restaurant revenue | Operating Segments | Restaurant Group          
Segment Reporting [Line Items]          
Total revenues 92.0 101.9 183.9 201.0  
Restaurant revenue | Operating Segments | Corporate and Other          
Segment Reporting [Line Items]          
Total revenues 0.0 0.0 0.0 0.0  
Other operating revenue          
Segment Reporting [Line Items]          
Total revenues 10.2 8.3 14.5 12.4  
Other operating revenue | Operating Segments | Total Reportable Segments          
Segment Reporting [Line Items]          
Total revenues 0.0 0.0 0.0 0.0  
Other operating revenue | Operating Segments | Restaurant Group          
Segment Reporting [Line Items]          
Total revenues 0.0 0.0 0.0 0.0  
Other operating revenue | Operating Segments | Corporate and Other          
Segment Reporting [Line Items]          
Total revenues $ 10.2 $ 8.3 $ 14.5 $ 12.4