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Simplifying (3x + -9)(8x + 6) = 0 Reorder the terms: (-9 + 3x)(8x + 6) = 0 Reorder the terms: (-9 + 3x)(6 + 8x) = 0 Multiply (-9 + 3x) * (6 + 8x) (-9(6 + 8x) + 3x * (6 + 8x)) = 0 ((6 * -9 + 8x * -9) + 3x * (6 + 8x)) = 0 ((-54 + -72x) + 3x * (6 + 8x)) = 0 (-54 + -72x + (6 * 3x + 8x * 3x)) = 0 (-54 + -72x + (18x + 24x2)) = 0 Combine like terms: -72x + 18x = -54x (-54 + -54x + 24x2) = 0 Solving -54 + -54x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + -9x + 4x2) = 0 Factor a trinomial. 6((-3 + -4x)(3 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 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 = {-0.75, 3}
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