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Simplifying (x + -6)(2x + 2) = (x + 3)(x + -4) Reorder the terms: (-6 + x)(2x + 2) = (x + 3)(x + -4) Reorder the terms: (-6 + x)(2 + 2x) = (x + 3)(x + -4) Multiply (-6 + x) * (2 + 2x) (-6(2 + 2x) + x(2 + 2x)) = (x + 3)(x + -4) ((2 * -6 + 2x * -6) + x(2 + 2x)) = (x + 3)(x + -4) ((-12 + -12x) + x(2 + 2x)) = (x + 3)(x + -4) (-12 + -12x + (2 * x + 2x * x)) = (x + 3)(x + -4) (-12 + -12x + (2x + 2x2)) = (x + 3)(x + -4) Combine like terms: -12x + 2x = -10x (-12 + -10x + 2x2) = (x + 3)(x + -4) Reorder the terms: -12 + -10x + 2x2 = (3 + x)(x + -4) Reorder the terms: -12 + -10x + 2x2 = (3 + x)(-4 + x) Multiply (3 + x) * (-4 + x) -12 + -10x + 2x2 = (3(-4 + x) + x(-4 + x)) -12 + -10x + 2x2 = ((-4 * 3 + x * 3) + x(-4 + x)) -12 + -10x + 2x2 = ((-12 + 3x) + x(-4 + x)) -12 + -10x + 2x2 = (-12 + 3x + (-4 * x + x * x)) -12 + -10x + 2x2 = (-12 + 3x + (-4x + x2)) Combine like terms: 3x + -4x = -1x -12 + -10x + 2x2 = (-12 + -1x + x2) Add '12' to each side of the equation. -12 + -10x + 12 + 2x2 = -12 + -1x + 12 + x2 Reorder the terms: -12 + 12 + -10x + 2x2 = -12 + -1x + 12 + x2 Combine like terms: -12 + 12 = 0 0 + -10x + 2x2 = -12 + -1x + 12 + x2 -10x + 2x2 = -12 + -1x + 12 + x2 Reorder the terms: -10x + 2x2 = -12 + 12 + -1x + x2 Combine like terms: -12 + 12 = 0 -10x + 2x2 = 0 + -1x + x2 -10x + 2x2 = -1x + x2 Solving -10x + 2x2 = -1x + x2 Solving for variable 'x'. Reorder the terms: -10x + x + 2x2 + -1x2 = -1x + x2 + x + -1x2 Combine like terms: -10x + x = -9x -9x + 2x2 + -1x2 = -1x + x2 + x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -9x + 1x2 = -1x + x2 + x + -1x2 Reorder the terms: -9x + 1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 -9x + 1x2 = 0 + x2 + -1x2 -9x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9Solution
x = {0, 9}
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