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Simplifying (2x + -2)(5x + 5) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) Reorder the terms: (-2 + 2x)(5x + 5) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) Reorder the terms: (-2 + 2x)(5 + 5x) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) Multiply (-2 + 2x) * (5 + 5x) (-2(5 + 5x) + 2x * (5 + 5x)) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) ((5 * -2 + 5x * -2) + 2x * (5 + 5x)) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) ((-10 + -10x) + 2x * (5 + 5x)) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) (-10 + -10x + (5 * 2x + 5x * 2x)) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) (-10 + -10x + (10x + 10x2)) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) Combine like terms: -10x + 10x = 0 (-10 + 0 + 10x2) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) (-10 + 10x2) + -1(x + -8)(-4x + -6) = (x + -8)(5x + 5) Reorder the terms: -10 + 10x2 + -1(-8 + x)(-4x + -6) = (x + -8)(5x + 5) Reorder the terms: -10 + 10x2 + -1(-8 + x)(-6 + -4x) = (x + -8)(5x + 5) Multiply (-8 + x) * (-6 + -4x) -10 + 10x2 + -1(-8(-6 + -4x) + x(-6 + -4x)) = (x + -8)(5x + 5) -10 + 10x2 + -1((-6 * -8 + -4x * -8) + x(-6 + -4x)) = (x + -8)(5x + 5) -10 + 10x2 + -1((48 + 32x) + x(-6 + -4x)) = (x + -8)(5x + 5) -10 + 10x2 + -1(48 + 32x + (-6 * x + -4x * x)) = (x + -8)(5x + 5) -10 + 10x2 + -1(48 + 32x + (-6x + -4x2)) = (x + -8)(5x + 5) Combine like terms: 32x + -6x = 26x -10 + 10x2 + -1(48 + 26x + -4x2) = (x + -8)(5x + 5) -10 + 10x2 + (48 * -1 + 26x * -1 + -4x2 * -1) = (x + -8)(5x + 5) -10 + 10x2 + (-48 + -26x + 4x2) = (x + -8)(5x + 5) Reorder the terms: -10 + -48 + -26x + 10x2 + 4x2 = (x + -8)(5x + 5) Combine like terms: -10 + -48 = -58 -58 + -26x + 10x2 + 4x2 = (x + -8)(5x + 5) Combine like terms: 10x2 + 4x2 = 14x2 -58 + -26x + 14x2 = (x + -8)(5x + 5) Reorder the terms: -58 + -26x + 14x2 = (-8 + x)(5x + 5) Reorder the terms: -58 + -26x + 14x2 = (-8 + x)(5 + 5x) Multiply (-8 + x) * (5 + 5x) -58 + -26x + 14x2 = (-8(5 + 5x) + x(5 + 5x)) -58 + -26x + 14x2 = ((5 * -8 + 5x * -8) + x(5 + 5x)) -58 + -26x + 14x2 = ((-40 + -40x) + x(5 + 5x)) -58 + -26x + 14x2 = (-40 + -40x + (5 * x + 5x * x)) -58 + -26x + 14x2 = (-40 + -40x + (5x + 5x2)) Combine like terms: -40x + 5x = -35x -58 + -26x + 14x2 = (-40 + -35x + 5x2) Solving -58 + -26x + 14x2 = -40 + -35x + 5x2 Solving for variable 'x'. Reorder the terms: -58 + 40 + -26x + 35x + 14x2 + -5x2 = -40 + -35x + 5x2 + 40 + 35x + -5x2 Combine like terms: -58 + 40 = -18 -18 + -26x + 35x + 14x2 + -5x2 = -40 + -35x + 5x2 + 40 + 35x + -5x2 Combine like terms: -26x + 35x = 9x -18 + 9x + 14x2 + -5x2 = -40 + -35x + 5x2 + 40 + 35x + -5x2 Combine like terms: 14x2 + -5x2 = 9x2 -18 + 9x + 9x2 = -40 + -35x + 5x2 + 40 + 35x + -5x2 Reorder the terms: -18 + 9x + 9x2 = -40 + 40 + -35x + 35x + 5x2 + -5x2 Combine like terms: -40 + 40 = 0 -18 + 9x + 9x2 = 0 + -35x + 35x + 5x2 + -5x2 -18 + 9x + 9x2 = -35x + 35x + 5x2 + -5x2 Combine like terms: -35x + 35x = 0 -18 + 9x + 9x2 = 0 + 5x2 + -5x2 -18 + 9x + 9x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -18 + 9x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-2 + x + x2) = 0 Factor a trinomial. 9((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 9.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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