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