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Simplifying 6(x + -1)(x + 2) + -1(1 + -1x)(2 + x) = 0 Reorder the terms: 6(-1 + x)(x + 2) + -1(1 + -1x)(2 + x) = 0 Reorder the terms: 6(-1 + x)(2 + x) + -1(1 + -1x)(2 + x) = 0 Multiply (-1 + x) * (2 + x) 6(-1(2 + x) + x(2 + x)) + -1(1 + -1x)(2 + x) = 0 6((2 * -1 + x * -1) + x(2 + x)) + -1(1 + -1x)(2 + x) = 0 6((-2 + -1x) + x(2 + x)) + -1(1 + -1x)(2 + x) = 0 6(-2 + -1x + (2 * x + x * x)) + -1(1 + -1x)(2 + x) = 0 6(-2 + -1x + (2x + x2)) + -1(1 + -1x)(2 + x) = 0 Combine like terms: -1x + 2x = 1x 6(-2 + 1x + x2) + -1(1 + -1x)(2 + x) = 0 (-2 * 6 + 1x * 6 + x2 * 6) + -1(1 + -1x)(2 + x) = 0 (-12 + 6x + 6x2) + -1(1 + -1x)(2 + x) = 0 Multiply (1 + -1x) * (2 + x) -12 + 6x + 6x2 + -1(1(2 + x) + -1x * (2 + x)) = 0 -12 + 6x + 6x2 + -1((2 * 1 + x * 1) + -1x * (2 + x)) = 0 -12 + 6x + 6x2 + -1((2 + 1x) + -1x * (2 + x)) = 0 -12 + 6x + 6x2 + -1(2 + 1x + (2 * -1x + x * -1x)) = 0 -12 + 6x + 6x2 + -1(2 + 1x + (-2x + -1x2)) = 0 Combine like terms: 1x + -2x = -1x -12 + 6x + 6x2 + -1(2 + -1x + -1x2) = 0 -12 + 6x + 6x2 + (2 * -1 + -1x * -1 + -1x2 * -1) = 0 -12 + 6x + 6x2 + (-2 + 1x + 1x2) = 0 Reorder the terms: -12 + -2 + 6x + 1x + 6x2 + 1x2 = 0 Combine like terms: -12 + -2 = -14 -14 + 6x + 1x + 6x2 + 1x2 = 0 Combine like terms: 6x + 1x = 7x -14 + 7x + 6x2 + 1x2 = 0 Combine like terms: 6x2 + 1x2 = 7x2 -14 + 7x + 7x2 = 0 Solving -14 + 7x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-2 + x + x2) = 0 Factor a trinomial. 7((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 7.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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