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Simplifying (2x + -3)(x + 4) = (x + -6)(x + 2) Reorder the terms: (-3 + 2x)(x + 4) = (x + -6)(x + 2) Reorder the terms: (-3 + 2x)(4 + x) = (x + -6)(x + 2) Multiply (-3 + 2x) * (4 + x) (-3(4 + x) + 2x * (4 + x)) = (x + -6)(x + 2) ((4 * -3 + x * -3) + 2x * (4 + x)) = (x + -6)(x + 2) ((-12 + -3x) + 2x * (4 + x)) = (x + -6)(x + 2) (-12 + -3x + (4 * 2x + x * 2x)) = (x + -6)(x + 2) (-12 + -3x + (8x + 2x2)) = (x + -6)(x + 2) Combine like terms: -3x + 8x = 5x (-12 + 5x + 2x2) = (x + -6)(x + 2) Reorder the terms: -12 + 5x + 2x2 = (-6 + x)(x + 2) Reorder the terms: -12 + 5x + 2x2 = (-6 + x)(2 + x) Multiply (-6 + x) * (2 + x) -12 + 5x + 2x2 = (-6(2 + x) + x(2 + x)) -12 + 5x + 2x2 = ((2 * -6 + x * -6) + x(2 + x)) -12 + 5x + 2x2 = ((-12 + -6x) + x(2 + x)) -12 + 5x + 2x2 = (-12 + -6x + (2 * x + x * x)) -12 + 5x + 2x2 = (-12 + -6x + (2x + x2)) Combine like terms: -6x + 2x = -4x -12 + 5x + 2x2 = (-12 + -4x + x2) Add '12' to each side of the equation. -12 + 5x + 12 + 2x2 = -12 + -4x + 12 + x2 Reorder the terms: -12 + 12 + 5x + 2x2 = -12 + -4x + 12 + x2 Combine like terms: -12 + 12 = 0 0 + 5x + 2x2 = -12 + -4x + 12 + x2 5x + 2x2 = -12 + -4x + 12 + x2 Reorder the terms: 5x + 2x2 = -12 + 12 + -4x + x2 Combine like terms: -12 + 12 = 0 5x + 2x2 = 0 + -4x + x2 5x + 2x2 = -4x + x2 Solving 5x + 2x2 = -4x + x2 Solving for variable 'x'. Reorder the terms: 5x + 4x + 2x2 + -1x2 = -4x + x2 + 4x + -1x2 Combine like terms: 5x + 4x = 9x 9x + 2x2 + -1x2 = -4x + x2 + 4x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 9x + 1x2 = -4x + x2 + 4x + -1x2 Reorder the terms: 9x + 1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 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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