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Simplifying x(x + 1) = (x + 5)(x + -2) Reorder the terms: x(1 + x) = (x + 5)(x + -2) (1 * x + x * x) = (x + 5)(x + -2) (1x + x2) = (x + 5)(x + -2) Reorder the terms: 1x + x2 = (5 + x)(x + -2) Reorder the terms: 1x + x2 = (5 + x)(-2 + x) Multiply (5 + x) * (-2 + x) 1x + x2 = (5(-2 + x) + x(-2 + x)) 1x + x2 = ((-2 * 5 + x * 5) + x(-2 + x)) 1x + x2 = ((-10 + 5x) + x(-2 + x)) 1x + x2 = (-10 + 5x + (-2 * x + x * x)) 1x + x2 = (-10 + 5x + (-2x + x2)) Combine like terms: 5x + -2x = 3x 1x + x2 = (-10 + 3x + x2) Add '-1x2' to each side of the equation. 1x + x2 + -1x2 = -10 + 3x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1x + 0 = -10 + 3x + x2 + -1x2 1x = -10 + 3x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1x = -10 + 3x + 0 1x = -10 + 3x Solving 1x = -10 + 3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3x' to each side of the equation. 1x + -3x = -10 + 3x + -3x Combine like terms: 1x + -3x = -2x -2x = -10 + 3x + -3x Combine like terms: 3x + -3x = 0 -2x = -10 + 0 -2x = -10 Divide each side by '-2'. x = 5 Simplifying x = 5
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