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Simplifying (x + -6)(2x + 2) = (x + 4)(x + -3) Reorder the terms: (-6 + x)(2x + 2) = (x + 4)(x + -3) Reorder the terms: (-6 + x)(2 + 2x) = (x + 4)(x + -3) Multiply (-6 + x) * (2 + 2x) (-6(2 + 2x) + x(2 + 2x)) = (x + 4)(x + -3) ((2 * -6 + 2x * -6) + x(2 + 2x)) = (x + 4)(x + -3) ((-12 + -12x) + x(2 + 2x)) = (x + 4)(x + -3) (-12 + -12x + (2 * x + 2x * x)) = (x + 4)(x + -3) (-12 + -12x + (2x + 2x2)) = (x + 4)(x + -3) Combine like terms: -12x + 2x = -10x (-12 + -10x + 2x2) = (x + 4)(x + -3) Reorder the terms: -12 + -10x + 2x2 = (4 + x)(x + -3) Reorder the terms: -12 + -10x + 2x2 = (4 + x)(-3 + x) Multiply (4 + x) * (-3 + x) -12 + -10x + 2x2 = (4(-3 + x) + x(-3 + x)) -12 + -10x + 2x2 = ((-3 * 4 + x * 4) + x(-3 + x)) -12 + -10x + 2x2 = ((-12 + 4x) + x(-3 + x)) -12 + -10x + 2x2 = (-12 + 4x + (-3 * x + x * x)) -12 + -10x + 2x2 = (-12 + 4x + (-3x + x2)) Combine like terms: 4x + -3x = 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 + -1x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: -10x + -1x = -11x -11x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -11x + 1x2 = 1x + x2 + -1x + -1x2 Reorder the terms: -11x + 1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 -11x + 1x2 = 0 + x2 + -1x2 -11x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -11x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 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 '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Simplifying x = 11Solution
x = {0, 11}
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