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Simplifying (x + -2)(x + -1) + (x + -2)(2x + 4) = 0 Reorder the terms: (-2 + x)(x + -1) + (x + -2)(2x + 4) = 0 Reorder the terms: (-2 + x)(-1 + x) + (x + -2)(2x + 4) = 0 Multiply (-2 + x) * (-1 + x) (-2(-1 + x) + x(-1 + x)) + (x + -2)(2x + 4) = 0 ((-1 * -2 + x * -2) + x(-1 + x)) + (x + -2)(2x + 4) = 0 ((2 + -2x) + x(-1 + x)) + (x + -2)(2x + 4) = 0 (2 + -2x + (-1 * x + x * x)) + (x + -2)(2x + 4) = 0 (2 + -2x + (-1x + x2)) + (x + -2)(2x + 4) = 0 Combine like terms: -2x + -1x = -3x (2 + -3x + x2) + (x + -2)(2x + 4) = 0 Reorder the terms: 2 + -3x + x2 + (-2 + x)(2x + 4) = 0 Reorder the terms: 2 + -3x + x2 + (-2 + x)(4 + 2x) = 0 Multiply (-2 + x) * (4 + 2x) 2 + -3x + x2 + (-2(4 + 2x) + x(4 + 2x)) = 0 2 + -3x + x2 + ((4 * -2 + 2x * -2) + x(4 + 2x)) = 0 2 + -3x + x2 + ((-8 + -4x) + x(4 + 2x)) = 0 2 + -3x + x2 + (-8 + -4x + (4 * x + 2x * x)) = 0 2 + -3x + x2 + (-8 + -4x + (4x + 2x2)) = 0 Combine like terms: -4x + 4x = 0 2 + -3x + x2 + (-8 + 0 + 2x2) = 0 2 + -3x + x2 + (-8 + 2x2) = 0 Reorder the terms: 2 + -8 + -3x + x2 + 2x2 = 0 Combine like terms: 2 + -8 = -6 -6 + -3x + x2 + 2x2 = 0 Combine like terms: x2 + 2x2 = 3x2 -6 + -3x + 3x2 = 0 Solving -6 + -3x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + -1x + x2) = 0 Factor a trinomial. 3((-1 + -1x)(2 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = -1Subproblem 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 = {-1, 2}
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