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Simplifying (3x + -9)(2x + -8) = 0 Reorder the terms: (-9 + 3x)(2x + -8) = 0 Reorder the terms: (-9 + 3x)(-8 + 2x) = 0 Multiply (-9 + 3x) * (-8 + 2x) (-9(-8 + 2x) + 3x * (-8 + 2x)) = 0 ((-8 * -9 + 2x * -9) + 3x * (-8 + 2x)) = 0 ((72 + -18x) + 3x * (-8 + 2x)) = 0 (72 + -18x + (-8 * 3x + 2x * 3x)) = 0 (72 + -18x + (-24x + 6x2)) = 0 Combine like terms: -18x + -24x = -42x (72 + -42x + 6x2) = 0 Solving 72 + -42x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(12 + -7x + x2) = 0 Factor a trinomial. 6((3 + -1x)(4 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 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 = {3, 4}
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