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Simplifying (2x + -6)(8x + 9) = 0 Reorder the terms: (-6 + 2x)(8x + 9) = 0 Reorder the terms: (-6 + 2x)(9 + 8x) = 0 Multiply (-6 + 2x) * (9 + 8x) (-6(9 + 8x) + 2x * (9 + 8x)) = 0 ((9 * -6 + 8x * -6) + 2x * (9 + 8x)) = 0 ((-54 + -48x) + 2x * (9 + 8x)) = 0 (-54 + -48x + (9 * 2x + 8x * 2x)) = 0 (-54 + -48x + (18x + 16x2)) = 0 Combine like terms: -48x + 18x = -30x (-54 + -30x + 16x2) = 0 Solving -54 + -30x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -15x + 8x2) = 0 Factor a trinomial. 2((-9 + -8x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -8x)' equal to zero and attempt to solve: Simplifying -9 + -8x = 0 Solving -9 + -8x = 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 + -8x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -8x = 0 + 9 -8x = 0 + 9 Combine like terms: 0 + 9 = 9 -8x = 9 Divide each side by '-8'. x = -1.125 Simplifying x = -1.125Subproblem 2
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 = 3Solution
x = {-1.125, 3}
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