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Simplifying (x + -2)(2x + -1) + (x + -2)(3x + -4) = 0 Reorder the terms: (-2 + x)(2x + -1) + (x + -2)(3x + -4) = 0 Reorder the terms: (-2 + x)(-1 + 2x) + (x + -2)(3x + -4) = 0 Multiply (-2 + x) * (-1 + 2x) (-2(-1 + 2x) + x(-1 + 2x)) + (x + -2)(3x + -4) = 0 ((-1 * -2 + 2x * -2) + x(-1 + 2x)) + (x + -2)(3x + -4) = 0 ((2 + -4x) + x(-1 + 2x)) + (x + -2)(3x + -4) = 0 (2 + -4x + (-1 * x + 2x * x)) + (x + -2)(3x + -4) = 0 (2 + -4x + (-1x + 2x2)) + (x + -2)(3x + -4) = 0 Combine like terms: -4x + -1x = -5x (2 + -5x + 2x2) + (x + -2)(3x + -4) = 0 Reorder the terms: 2 + -5x + 2x2 + (-2 + x)(3x + -4) = 0 Reorder the terms: 2 + -5x + 2x2 + (-2 + x)(-4 + 3x) = 0 Multiply (-2 + x) * (-4 + 3x) 2 + -5x + 2x2 + (-2(-4 + 3x) + x(-4 + 3x)) = 0 2 + -5x + 2x2 + ((-4 * -2 + 3x * -2) + x(-4 + 3x)) = 0 2 + -5x + 2x2 + ((8 + -6x) + x(-4 + 3x)) = 0 2 + -5x + 2x2 + (8 + -6x + (-4 * x + 3x * x)) = 0 2 + -5x + 2x2 + (8 + -6x + (-4x + 3x2)) = 0 Combine like terms: -6x + -4x = -10x 2 + -5x + 2x2 + (8 + -10x + 3x2) = 0 Reorder the terms: 2 + 8 + -5x + -10x + 2x2 + 3x2 = 0 Combine like terms: 2 + 8 = 10 10 + -5x + -10x + 2x2 + 3x2 = 0 Combine like terms: -5x + -10x = -15x 10 + -15x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 10 + -15x + 5x2 = 0 Solving 10 + -15x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -3x + x2) = 0 Factor a trinomial. 5((1 + -1x)(2 + -1x)) = 0 Ignore the factor 5.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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