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