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Simplifying (3x + -3)(x + -1) + 5 = 32 Reorder the terms: (-3 + 3x)(x + -1) + 5 = 32 Reorder the terms: (-3 + 3x)(-1 + x) + 5 = 32 Multiply (-3 + 3x) * (-1 + x) (-3(-1 + x) + 3x * (-1 + x)) + 5 = 32 ((-1 * -3 + x * -3) + 3x * (-1 + x)) + 5 = 32 ((3 + -3x) + 3x * (-1 + x)) + 5 = 32 (3 + -3x + (-1 * 3x + x * 3x)) + 5 = 32 (3 + -3x + (-3x + 3x2)) + 5 = 32 Combine like terms: -3x + -3x = -6x (3 + -6x + 3x2) + 5 = 32 Reorder the terms: 3 + 5 + -6x + 3x2 = 32 Combine like terms: 3 + 5 = 8 8 + -6x + 3x2 = 32 Solving 8 + -6x + 3x2 = 32 Solving for variable 'x'. Reorder the terms: 8 + -32 + -6x + 3x2 = 32 + -32 Combine like terms: 8 + -32 = -24 -24 + -6x + 3x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -24 + -6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -2x + x2) = 0 Factor a trinomial. 3((-2 + -1x)(4 + -1x)) = 0 Ignore the factor 3.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-2, 4}
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