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Simplifying (2x + -3)(x + 6) = (x + -6)(x + 3) Reorder the terms: (-3 + 2x)(x + 6) = (x + -6)(x + 3) Reorder the terms: (-3 + 2x)(6 + x) = (x + -6)(x + 3) Multiply (-3 + 2x) * (6 + x) (-3(6 + x) + 2x * (6 + x)) = (x + -6)(x + 3) ((6 * -3 + x * -3) + 2x * (6 + x)) = (x + -6)(x + 3) ((-18 + -3x) + 2x * (6 + x)) = (x + -6)(x + 3) (-18 + -3x + (6 * 2x + x * 2x)) = (x + -6)(x + 3) (-18 + -3x + (12x + 2x2)) = (x + -6)(x + 3) Combine like terms: -3x + 12x = 9x (-18 + 9x + 2x2) = (x + -6)(x + 3) Reorder the terms: -18 + 9x + 2x2 = (-6 + x)(x + 3) Reorder the terms: -18 + 9x + 2x2 = (-6 + x)(3 + x) Multiply (-6 + x) * (3 + x) -18 + 9x + 2x2 = (-6(3 + x) + x(3 + x)) -18 + 9x + 2x2 = ((3 * -6 + x * -6) + x(3 + x)) -18 + 9x + 2x2 = ((-18 + -6x) + x(3 + x)) -18 + 9x + 2x2 = (-18 + -6x + (3 * x + x * x)) -18 + 9x + 2x2 = (-18 + -6x + (3x + x2)) Combine like terms: -6x + 3x = -3x -18 + 9x + 2x2 = (-18 + -3x + x2) Add '18' to each side of the equation. -18 + 9x + 18 + 2x2 = -18 + -3x + 18 + x2 Reorder the terms: -18 + 18 + 9x + 2x2 = -18 + -3x + 18 + x2 Combine like terms: -18 + 18 = 0 0 + 9x + 2x2 = -18 + -3x + 18 + x2 9x + 2x2 = -18 + -3x + 18 + x2 Reorder the terms: 9x + 2x2 = -18 + 18 + -3x + x2 Combine like terms: -18 + 18 = 0 9x + 2x2 = 0 + -3x + x2 9x + 2x2 = -3x + x2 Solving 9x + 2x2 = -3x + x2 Solving for variable 'x'. Reorder the terms: 9x + 3x + 2x2 + -1x2 = -3x + x2 + 3x + -1x2 Combine like terms: 9x + 3x = 12x 12x + 2x2 + -1x2 = -3x + x2 + 3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 12x + 1x2 = -3x + x2 + 3x + -1x2 Reorder the terms: 12x + 1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 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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