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Simplifying (3x + 3)(x + -2) + -1(x + -5)(x + -2) = 0 Reorder the terms: (3 + 3x)(x + -2) + -1(x + -5)(x + -2) = 0 Reorder the terms: (3 + 3x)(-2 + x) + -1(x + -5)(x + -2) = 0 Multiply (3 + 3x) * (-2 + x) (3(-2 + x) + 3x * (-2 + x)) + -1(x + -5)(x + -2) = 0 ((-2 * 3 + x * 3) + 3x * (-2 + x)) + -1(x + -5)(x + -2) = 0 ((-6 + 3x) + 3x * (-2 + x)) + -1(x + -5)(x + -2) = 0 (-6 + 3x + (-2 * 3x + x * 3x)) + -1(x + -5)(x + -2) = 0 (-6 + 3x + (-6x + 3x2)) + -1(x + -5)(x + -2) = 0 Combine like terms: 3x + -6x = -3x (-6 + -3x + 3x2) + -1(x + -5)(x + -2) = 0 Reorder the terms: -6 + -3x + 3x2 + -1(-5 + x)(x + -2) = 0 Reorder the terms: -6 + -3x + 3x2 + -1(-5 + x)(-2 + x) = 0 Multiply (-5 + x) * (-2 + x) -6 + -3x + 3x2 + -1(-5(-2 + x) + x(-2 + x)) = 0 -6 + -3x + 3x2 + -1((-2 * -5 + x * -5) + x(-2 + x)) = 0 -6 + -3x + 3x2 + -1((10 + -5x) + x(-2 + x)) = 0 -6 + -3x + 3x2 + -1(10 + -5x + (-2 * x + x * x)) = 0 -6 + -3x + 3x2 + -1(10 + -5x + (-2x + x2)) = 0 Combine like terms: -5x + -2x = -7x -6 + -3x + 3x2 + -1(10 + -7x + x2) = 0 -6 + -3x + 3x2 + (10 * -1 + -7x * -1 + x2 * -1) = 0 -6 + -3x + 3x2 + (-10 + 7x + -1x2) = 0 Reorder the terms: -6 + -10 + -3x + 7x + 3x2 + -1x2 = 0 Combine like terms: -6 + -10 = -16 -16 + -3x + 7x + 3x2 + -1x2 = 0 Combine like terms: -3x + 7x = 4x -16 + 4x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 -16 + 4x + 2x2 = 0 Solving -16 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 2x + x2) = 0 Factor a trinomial. 2((-4 + -1x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-4, 2}
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