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Simplifying (x + -4)(2x + 3) + -1(8 + x) = 0 Reorder the terms: (-4 + x)(2x + 3) + -1(8 + x) = 0 Reorder the terms: (-4 + x)(3 + 2x) + -1(8 + x) = 0 Multiply (-4 + x) * (3 + 2x) (-4(3 + 2x) + x(3 + 2x)) + -1(8 + x) = 0 ((3 * -4 + 2x * -4) + x(3 + 2x)) + -1(8 + x) = 0 ((-12 + -8x) + x(3 + 2x)) + -1(8 + x) = 0 (-12 + -8x + (3 * x + 2x * x)) + -1(8 + x) = 0 (-12 + -8x + (3x + 2x2)) + -1(8 + x) = 0 Combine like terms: -8x + 3x = -5x (-12 + -5x + 2x2) + -1(8 + x) = 0 -12 + -5x + 2x2 + (8 * -1 + x * -1) = 0 -12 + -5x + 2x2 + (-8 + -1x) = 0 Reorder the terms: -12 + -8 + -5x + -1x + 2x2 = 0 Combine like terms: -12 + -8 = -20 -20 + -5x + -1x + 2x2 = 0 Combine like terms: -5x + -1x = -6x -20 + -6x + 2x2 = 0 Solving -20 + -6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -3x + x2) = 0 Factor a trinomial. 2((-2 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-2, 5}
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