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