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Simplifying (x + -1)(2x + 3) + -1(x + -1)(x + -6) = 0 Reorder the terms: (-1 + x)(2x + 3) + -1(x + -1)(x + -6) = 0 Reorder the terms: (-1 + x)(3 + 2x) + -1(x + -1)(x + -6) = 0 Multiply (-1 + x) * (3 + 2x) (-1(3 + 2x) + x(3 + 2x)) + -1(x + -1)(x + -6) = 0 ((3 * -1 + 2x * -1) + x(3 + 2x)) + -1(x + -1)(x + -6) = 0 ((-3 + -2x) + x(3 + 2x)) + -1(x + -1)(x + -6) = 0 (-3 + -2x + (3 * x + 2x * x)) + -1(x + -1)(x + -6) = 0 (-3 + -2x + (3x + 2x2)) + -1(x + -1)(x + -6) = 0 Combine like terms: -2x + 3x = 1x (-3 + 1x + 2x2) + -1(x + -1)(x + -6) = 0 Reorder the terms: -3 + 1x + 2x2 + -1(-1 + x)(x + -6) = 0 Reorder the terms: -3 + 1x + 2x2 + -1(-1 + x)(-6 + x) = 0 Multiply (-1 + x) * (-6 + x) -3 + 1x + 2x2 + -1(-1(-6 + x) + x(-6 + x)) = 0 -3 + 1x + 2x2 + -1((-6 * -1 + x * -1) + x(-6 + x)) = 0 -3 + 1x + 2x2 + -1((6 + -1x) + x(-6 + x)) = 0 -3 + 1x + 2x2 + -1(6 + -1x + (-6 * x + x * x)) = 0 -3 + 1x + 2x2 + -1(6 + -1x + (-6x + x2)) = 0 Combine like terms: -1x + -6x = -7x -3 + 1x + 2x2 + -1(6 + -7x + x2) = 0 -3 + 1x + 2x2 + (6 * -1 + -7x * -1 + x2 * -1) = 0 -3 + 1x + 2x2 + (-6 + 7x + -1x2) = 0 Reorder the terms: -3 + -6 + 1x + 7x + 2x2 + -1x2 = 0 Combine like terms: -3 + -6 = -9 -9 + 1x + 7x + 2x2 + -1x2 = 0 Combine like terms: 1x + 7x = 8x -9 + 8x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -9 + 8x + 1x2 = 0 Solving -9 + 8x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-9 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 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 = {-9, 1}
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