| 100 | Y | − | ( | 580 | + | 40 | × | 100 | ) | − | ( | 100 | Y | × | 13 100 | + | 5 | × | 100 | ) | × | 12 100 | = | 0 |
| Left side of the equation = | 100 | Y | − | 580 | − | 40 | × | 100 | − | ( | 100 | Y | × | 13 100 | + | 5 | × | 100 | ) | × | 12 100 |
| = | 100 | Y | − | 580 | − | 4000 | − | ( | 100 | Y | × | 13 100 | + | 5 | × | 100 | ) | × | 12 100 |
| = | 100 | Y | − | 4580 | − | ( | 100 | Y | × | 13 100 | + | 5 | × | 100 | ) | × | 12 100 |
| = | 100 | Y | − | 4580 | − | 100 | Y | × | 13 100 | × | 12 100 | − | 5 | × | 100 | × | 12 100 |
| = | 100 | Y | − | 4580 | − | 39 25 | Y | − | 60 |
| = | 2461 25 | Y | − | 4640 |
2461 25 | Y | − | 4640 | = | 0 |
2461 25 | Y | = | 0 | + | 4640 |
2461 25 | Y | = | 4640 |
| Y | = | 4640 | ÷ | 2461 25 |
| = | 4640 | × | 25 2461 |
| Y | = | 116000 2461 |
| Y | = | 47.135311 |