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Simplifying (x + -6)(2x + 4) = (x + 8)(x + -3) Reorder the terms: (-6 + x)(2x + 4) = (x + 8)(x + -3) Reorder the terms: (-6 + x)(4 + 2x) = (x + 8)(x + -3) Multiply (-6 + x) * (4 + 2x) (-6(4 + 2x) + x(4 + 2x)) = (x + 8)(x + -3) ((4 * -6 + 2x * -6) + x(4 + 2x)) = (x + 8)(x + -3) ((-24 + -12x) + x(4 + 2x)) = (x + 8)(x + -3) (-24 + -12x + (4 * x + 2x * x)) = (x + 8)(x + -3) (-24 + -12x + (4x + 2x2)) = (x + 8)(x + -3) Combine like terms: -12x + 4x = -8x (-24 + -8x + 2x2) = (x + 8)(x + -3) Reorder the terms: -24 + -8x + 2x2 = (8 + x)(x + -3) Reorder the terms: -24 + -8x + 2x2 = (8 + x)(-3 + x) Multiply (8 + x) * (-3 + x) -24 + -8x + 2x2 = (8(-3 + x) + x(-3 + x)) -24 + -8x + 2x2 = ((-3 * 8 + x * 8) + x(-3 + x)) -24 + -8x + 2x2 = ((-24 + 8x) + x(-3 + x)) -24 + -8x + 2x2 = (-24 + 8x + (-3 * x + x * x)) -24 + -8x + 2x2 = (-24 + 8x + (-3x + x2)) Combine like terms: 8x + -3x = 5x -24 + -8x + 2x2 = (-24 + 5x + x2) Add '24' to each side of the equation. -24 + -8x + 24 + 2x2 = -24 + 5x + 24 + x2 Reorder the terms: -24 + 24 + -8x + 2x2 = -24 + 5x + 24 + x2 Combine like terms: -24 + 24 = 0 0 + -8x + 2x2 = -24 + 5x + 24 + x2 -8x + 2x2 = -24 + 5x + 24 + x2 Reorder the terms: -8x + 2x2 = -24 + 24 + 5x + x2 Combine like terms: -24 + 24 = 0 -8x + 2x2 = 0 + 5x + x2 -8x + 2x2 = 5x + x2 Solving -8x + 2x2 = 5x + x2 Solving for variable 'x'. Reorder the terms: -8x + -5x + 2x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: -8x + -5x = -13x -13x + 2x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -13x + 1x2 = 5x + x2 + -5x + -1x2 Reorder the terms: -13x + 1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 -13x + 1x2 = 0 + x2 + -1x2 -13x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -13x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-13 + 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 '(-13 + x)' equal to zero and attempt to solve: Simplifying -13 + x = 0 Solving -13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + x = 0 + 13 x = 0 + 13 Combine like terms: 0 + 13 = 13 x = 13 Simplifying x = 13Solution
x = {0, 13}
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