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Simplifying (x + -6)(3x + -2) + -1(x + 4)(x + -2) = 0 Reorder the terms: (-6 + x)(3x + -2) + -1(x + 4)(x + -2) = 0 Reorder the terms: (-6 + x)(-2 + 3x) + -1(x + 4)(x + -2) = 0 Multiply (-6 + x) * (-2 + 3x) (-6(-2 + 3x) + x(-2 + 3x)) + -1(x + 4)(x + -2) = 0 ((-2 * -6 + 3x * -6) + x(-2 + 3x)) + -1(x + 4)(x + -2) = 0 ((12 + -18x) + x(-2 + 3x)) + -1(x + 4)(x + -2) = 0 (12 + -18x + (-2 * x + 3x * x)) + -1(x + 4)(x + -2) = 0 (12 + -18x + (-2x + 3x2)) + -1(x + 4)(x + -2) = 0 Combine like terms: -18x + -2x = -20x (12 + -20x + 3x2) + -1(x + 4)(x + -2) = 0 Reorder the terms: 12 + -20x + 3x2 + -1(4 + x)(x + -2) = 0 Reorder the terms: 12 + -20x + 3x2 + -1(4 + x)(-2 + x) = 0 Multiply (4 + x) * (-2 + x) 12 + -20x + 3x2 + -1(4(-2 + x) + x(-2 + x)) = 0 12 + -20x + 3x2 + -1((-2 * 4 + x * 4) + x(-2 + x)) = 0 12 + -20x + 3x2 + -1((-8 + 4x) + x(-2 + x)) = 0 12 + -20x + 3x2 + -1(-8 + 4x + (-2 * x + x * x)) = 0 12 + -20x + 3x2 + -1(-8 + 4x + (-2x + x2)) = 0 Combine like terms: 4x + -2x = 2x 12 + -20x + 3x2 + -1(-8 + 2x + x2) = 0 12 + -20x + 3x2 + (-8 * -1 + 2x * -1 + x2 * -1) = 0 12 + -20x + 3x2 + (8 + -2x + -1x2) = 0 Reorder the terms: 12 + 8 + -20x + -2x + 3x2 + -1x2 = 0 Combine like terms: 12 + 8 = 20 20 + -20x + -2x + 3x2 + -1x2 = 0 Combine like terms: -20x + -2x = -22x 20 + -22x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 20 + -22x + 2x2 = 0 Solving 20 + -22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -11x + x2) = 0 Factor a trinomial. 2((1 + -1x)(10 + -1x)) = 0 Ignore the factor 2.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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {1, 10}
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