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Simplifying (x + -1)(x + -2) = 5(x + -1) Reorder the terms: (-1 + x)(x + -2) = 5(x + -1) Reorder the terms: (-1 + x)(-2 + x) = 5(x + -1) Multiply (-1 + x) * (-2 + x) (-1(-2 + x) + x(-2 + x)) = 5(x + -1) ((-2 * -1 + x * -1) + x(-2 + x)) = 5(x + -1) ((2 + -1x) + x(-2 + x)) = 5(x + -1) (2 + -1x + (-2 * x + x * x)) = 5(x + -1) (2 + -1x + (-2x + x2)) = 5(x + -1) Combine like terms: -1x + -2x = -3x (2 + -3x + x2) = 5(x + -1) Reorder the terms: 2 + -3x + x2 = 5(-1 + x) 2 + -3x + x2 = (-1 * 5 + x * 5) 2 + -3x + x2 = (-5 + 5x) Solving 2 + -3x + x2 = -5 + 5x Solving for variable 'x'. Reorder the terms: 2 + 5 + -3x + -5x + x2 = -5 + 5x + 5 + -5x Combine like terms: 2 + 5 = 7 7 + -3x + -5x + x2 = -5 + 5x + 5 + -5x Combine like terms: -3x + -5x = -8x 7 + -8x + x2 = -5 + 5x + 5 + -5x Reorder the terms: 7 + -8x + x2 = -5 + 5 + 5x + -5x Combine like terms: -5 + 5 = 0 7 + -8x + x2 = 0 + 5x + -5x 7 + -8x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 7 + -8x + x2 = 0 Factor a trinomial. (1 + -1x)(7 + -1x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {1, 7}
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