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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 = 1x (-2 + 1x + x2) = 5(x + -1) Reorder the terms: -2 + 1x + x2 = 5(-1 + x) -2 + 1x + x2 = (-1 * 5 + x * 5) -2 + 1x + x2 = (-5 + 5x) Solving -2 + 1x + x2 = -5 + 5x Solving for variable 'x'. Reorder the terms: -2 + 5 + 1x + -5x + x2 = -5 + 5x + 5 + -5x Combine like terms: -2 + 5 = 3 3 + 1x + -5x + x2 = -5 + 5x + 5 + -5x Combine like terms: 1x + -5x = -4x 3 + -4x + x2 = -5 + 5x + 5 + -5x Reorder the terms: 3 + -4x + x2 = -5 + 5 + 5x + -5x Combine like terms: -5 + 5 = 0 3 + -4x + x2 = 0 + 5x + -5x 3 + -4x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 3 + -4x + x2 = 0 Factor a trinomial. (1 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {1, 3}
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