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Simplifying (2x + -3)(x + 8) = (x + -6)(x + 4) Reorder the terms: (-3 + 2x)(x + 8) = (x + -6)(x + 4) Reorder the terms: (-3 + 2x)(8 + x) = (x + -6)(x + 4) Multiply (-3 + 2x) * (8 + x) (-3(8 + x) + 2x * (8 + x)) = (x + -6)(x + 4) ((8 * -3 + x * -3) + 2x * (8 + x)) = (x + -6)(x + 4) ((-24 + -3x) + 2x * (8 + x)) = (x + -6)(x + 4) (-24 + -3x + (8 * 2x + x * 2x)) = (x + -6)(x + 4) (-24 + -3x + (16x + 2x2)) = (x + -6)(x + 4) Combine like terms: -3x + 16x = 13x (-24 + 13x + 2x2) = (x + -6)(x + 4) Reorder the terms: -24 + 13x + 2x2 = (-6 + x)(x + 4) Reorder the terms: -24 + 13x + 2x2 = (-6 + x)(4 + x) Multiply (-6 + x) * (4 + x) -24 + 13x + 2x2 = (-6(4 + x) + x(4 + x)) -24 + 13x + 2x2 = ((4 * -6 + x * -6) + x(4 + x)) -24 + 13x + 2x2 = ((-24 + -6x) + x(4 + x)) -24 + 13x + 2x2 = (-24 + -6x + (4 * x + x * x)) -24 + 13x + 2x2 = (-24 + -6x + (4x + x2)) Combine like terms: -6x + 4x = -2x -24 + 13x + 2x2 = (-24 + -2x + x2) Add '24' to each side of the equation. -24 + 13x + 24 + 2x2 = -24 + -2x + 24 + x2 Reorder the terms: -24 + 24 + 13x + 2x2 = -24 + -2x + 24 + x2 Combine like terms: -24 + 24 = 0 0 + 13x + 2x2 = -24 + -2x + 24 + x2 13x + 2x2 = -24 + -2x + 24 + x2 Reorder the terms: 13x + 2x2 = -24 + 24 + -2x + x2 Combine like terms: -24 + 24 = 0 13x + 2x2 = 0 + -2x + x2 13x + 2x2 = -2x + x2 Solving 13x + 2x2 = -2x + x2 Solving for variable 'x'. Reorder the terms: 13x + 2x + 2x2 + -1x2 = -2x + x2 + 2x + -1x2 Combine like terms: 13x + 2x = 15x 15x + 2x2 + -1x2 = -2x + x2 + 2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 15x + 1x2 = -2x + x2 + 2x + -1x2 Reorder the terms: 15x + 1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 15x + 1x2 = 0 + x2 + -1x2 15x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(15 + 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 '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Solution
x = {0, -15}
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