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Simplifying (x + -6)(2x + 6) = (x + 9)(x + -4) Reorder the terms: (-6 + x)(2x + 6) = (x + 9)(x + -4) Reorder the terms: (-6 + x)(6 + 2x) = (x + 9)(x + -4) Multiply (-6 + x) * (6 + 2x) (-6(6 + 2x) + x(6 + 2x)) = (x + 9)(x + -4) ((6 * -6 + 2x * -6) + x(6 + 2x)) = (x + 9)(x + -4) ((-36 + -12x) + x(6 + 2x)) = (x + 9)(x + -4) (-36 + -12x + (6 * x + 2x * x)) = (x + 9)(x + -4) (-36 + -12x + (6x + 2x2)) = (x + 9)(x + -4) Combine like terms: -12x + 6x = -6x (-36 + -6x + 2x2) = (x + 9)(x + -4) Reorder the terms: -36 + -6x + 2x2 = (9 + x)(x + -4) Reorder the terms: -36 + -6x + 2x2 = (9 + x)(-4 + x) Multiply (9 + x) * (-4 + x) -36 + -6x + 2x2 = (9(-4 + x) + x(-4 + x)) -36 + -6x + 2x2 = ((-4 * 9 + x * 9) + x(-4 + x)) -36 + -6x + 2x2 = ((-36 + 9x) + x(-4 + x)) -36 + -6x + 2x2 = (-36 + 9x + (-4 * x + x * x)) -36 + -6x + 2x2 = (-36 + 9x + (-4x + x2)) Combine like terms: 9x + -4x = 5x -36 + -6x + 2x2 = (-36 + 5x + x2) Add '36' to each side of the equation. -36 + -6x + 36 + 2x2 = -36 + 5x + 36 + x2 Reorder the terms: -36 + 36 + -6x + 2x2 = -36 + 5x + 36 + x2 Combine like terms: -36 + 36 = 0 0 + -6x + 2x2 = -36 + 5x + 36 + x2 -6x + 2x2 = -36 + 5x + 36 + x2 Reorder the terms: -6x + 2x2 = -36 + 36 + 5x + x2 Combine like terms: -36 + 36 = 0 -6x + 2x2 = 0 + 5x + x2 -6x + 2x2 = 5x + x2 Solving -6x + 2x2 = 5x + x2 Solving for variable 'x'. Reorder the terms: -6x + -5x + 2x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: -6x + -5x = -11x -11x + 2x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -11x + 1x2 = 5x + x2 + -5x + -1x2 Reorder the terms: -11x + 1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 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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