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Simplifying 4x(x + -12) = (5x + -6)(x + -6) Reorder the terms: 4x(-12 + x) = (5x + -6)(x + -6) (-12 * 4x + x * 4x) = (5x + -6)(x + -6) (-48x + 4x2) = (5x + -6)(x + -6) Reorder the terms: -48x + 4x2 = (-6 + 5x)(x + -6) Reorder the terms: -48x + 4x2 = (-6 + 5x)(-6 + x) Multiply (-6 + 5x) * (-6 + x) -48x + 4x2 = (-6(-6 + x) + 5x * (-6 + x)) -48x + 4x2 = ((-6 * -6 + x * -6) + 5x * (-6 + x)) -48x + 4x2 = ((36 + -6x) + 5x * (-6 + x)) -48x + 4x2 = (36 + -6x + (-6 * 5x + x * 5x)) -48x + 4x2 = (36 + -6x + (-30x + 5x2)) Combine like terms: -6x + -30x = -36x -48x + 4x2 = (36 + -36x + 5x2) Solving -48x + 4x2 = 36 + -36x + 5x2 Solving for variable 'x'. Reorder the terms: -36 + -48x + 36x + 4x2 + -5x2 = 36 + -36x + 5x2 + -36 + 36x + -5x2 Combine like terms: -48x + 36x = -12x -36 + -12x + 4x2 + -5x2 = 36 + -36x + 5x2 + -36 + 36x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -36 + -12x + -1x2 = 36 + -36x + 5x2 + -36 + 36x + -5x2 Reorder the terms: -36 + -12x + -1x2 = 36 + -36 + -36x + 36x + 5x2 + -5x2 Combine like terms: 36 + -36 = 0 -36 + -12x + -1x2 = 0 + -36x + 36x + 5x2 + -5x2 -36 + -12x + -1x2 = -36x + 36x + 5x2 + -5x2 Combine like terms: -36x + 36x = 0 -36 + -12x + -1x2 = 0 + 5x2 + -5x2 -36 + -12x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -36 + -12x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(36 + 12x + x2) = 0 Factor a trinomial. -1((6 + x)(6 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {-6, -6}
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