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Simplifying (3x + 6)(3x + -1) + -1(3x + 6)(2x + -4) = 0 Reorder the terms: (6 + 3x)(3x + -1) + -1(3x + 6)(2x + -4) = 0 Reorder the terms: (6 + 3x)(-1 + 3x) + -1(3x + 6)(2x + -4) = 0 Multiply (6 + 3x) * (-1 + 3x) (6(-1 + 3x) + 3x * (-1 + 3x)) + -1(3x + 6)(2x + -4) = 0 ((-1 * 6 + 3x * 6) + 3x * (-1 + 3x)) + -1(3x + 6)(2x + -4) = 0 ((-6 + 18x) + 3x * (-1 + 3x)) + -1(3x + 6)(2x + -4) = 0 (-6 + 18x + (-1 * 3x + 3x * 3x)) + -1(3x + 6)(2x + -4) = 0 (-6 + 18x + (-3x + 9x2)) + -1(3x + 6)(2x + -4) = 0 Combine like terms: 18x + -3x = 15x (-6 + 15x + 9x2) + -1(3x + 6)(2x + -4) = 0 Reorder the terms: -6 + 15x + 9x2 + -1(6 + 3x)(2x + -4) = 0 Reorder the terms: -6 + 15x + 9x2 + -1(6 + 3x)(-4 + 2x) = 0 Multiply (6 + 3x) * (-4 + 2x) -6 + 15x + 9x2 + -1(6(-4 + 2x) + 3x * (-4 + 2x)) = 0 -6 + 15x + 9x2 + -1((-4 * 6 + 2x * 6) + 3x * (-4 + 2x)) = 0 -6 + 15x + 9x2 + -1((-24 + 12x) + 3x * (-4 + 2x)) = 0 -6 + 15x + 9x2 + -1(-24 + 12x + (-4 * 3x + 2x * 3x)) = 0 -6 + 15x + 9x2 + -1(-24 + 12x + (-12x + 6x2)) = 0 Combine like terms: 12x + -12x = 0 -6 + 15x + 9x2 + -1(-24 + 0 + 6x2) = 0 -6 + 15x + 9x2 + -1(-24 + 6x2) = 0 -6 + 15x + 9x2 + (-24 * -1 + 6x2 * -1) = 0 -6 + 15x + 9x2 + (24 + -6x2) = 0 Reorder the terms: -6 + 24 + 15x + 9x2 + -6x2 = 0 Combine like terms: -6 + 24 = 18 18 + 15x + 9x2 + -6x2 = 0 Combine like terms: 9x2 + -6x2 = 3x2 18 + 15x + 3x2 = 0 Solving 18 + 15x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 5x + x2) = 0 Factor a trinomial. 3((3 + x)(2 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-3, -2}
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