| ( | 1000 | − | x | ) | ( | 1000 | − | x | ) | = | 100 | x |
| Left side of the equation = | 1000 | ( | 1000 | − | x | ) | − | x | ( | 1000 | − | x | ) |
| = | 1000 | × | 1000 | − | 1000 | x | − | x | ( | 1000 | − | x | ) |
| = | 1000000 | − | 1000 | x | − | x | ( | 1000 | − | x | ) |
| = | 1000000 | − | 1000 | x | − | x | × | 1000 | + | x | x |
| = | 1000000 | − | 2000 | x | + | x | x |
| 1000000 | − | 2000 | x | + | x | x | = | 100 | x |