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Simplifying (2x + -1)(x + 6) = (x + -2)(x + 3) Reorder the terms: (-1 + 2x)(x + 6) = (x + -2)(x + 3) Reorder the terms: (-1 + 2x)(6 + x) = (x + -2)(x + 3) Multiply (-1 + 2x) * (6 + x) (-1(6 + x) + 2x * (6 + x)) = (x + -2)(x + 3) ((6 * -1 + x * -1) + 2x * (6 + x)) = (x + -2)(x + 3) ((-6 + -1x) + 2x * (6 + x)) = (x + -2)(x + 3) (-6 + -1x + (6 * 2x + x * 2x)) = (x + -2)(x + 3) (-6 + -1x + (12x + 2x2)) = (x + -2)(x + 3) Combine like terms: -1x + 12x = 11x (-6 + 11x + 2x2) = (x + -2)(x + 3) Reorder the terms: -6 + 11x + 2x2 = (-2 + x)(x + 3) Reorder the terms: -6 + 11x + 2x2 = (-2 + x)(3 + x) Multiply (-2 + x) * (3 + x) -6 + 11x + 2x2 = (-2(3 + x) + x(3 + x)) -6 + 11x + 2x2 = ((3 * -2 + x * -2) + x(3 + x)) -6 + 11x + 2x2 = ((-6 + -2x) + x(3 + x)) -6 + 11x + 2x2 = (-6 + -2x + (3 * x + x * x)) -6 + 11x + 2x2 = (-6 + -2x + (3x + x2)) Combine like terms: -2x + 3x = 1x -6 + 11x + 2x2 = (-6 + 1x + x2) Add '6' to each side of the equation. -6 + 11x + 6 + 2x2 = -6 + 1x + 6 + x2 Reorder the terms: -6 + 6 + 11x + 2x2 = -6 + 1x + 6 + x2 Combine like terms: -6 + 6 = 0 0 + 11x + 2x2 = -6 + 1x + 6 + x2 11x + 2x2 = -6 + 1x + 6 + x2 Reorder the terms: 11x + 2x2 = -6 + 6 + 1x + x2 Combine like terms: -6 + 6 = 0 11x + 2x2 = 0 + 1x + x2 11x + 2x2 = 1x + x2 Solving 11x + 2x2 = 1x + x2 Solving for variable 'x'. Reorder the terms: 11x + -1x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: 11x + -1x = 10x 10x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 10x + 1x2 = 1x + x2 + -1x + -1x2 Reorder the terms: 10x + 1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 10x + 1x2 = 0 + x2 + -1x2 10x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(10 + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {0, -10}
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