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Simplifying (5x + 6)(3x + -9) = 0 Reorder the terms: (6 + 5x)(3x + -9) = 0 Reorder the terms: (6 + 5x)(-9 + 3x) = 0 Multiply (6 + 5x) * (-9 + 3x) (6(-9 + 3x) + 5x * (-9 + 3x)) = 0 ((-9 * 6 + 3x * 6) + 5x * (-9 + 3x)) = 0 ((-54 + 18x) + 5x * (-9 + 3x)) = 0 (-54 + 18x + (-9 * 5x + 3x * 5x)) = 0 (-54 + 18x + (-45x + 15x2)) = 0 Combine like terms: 18x + -45x = -27x (-54 + -27x + 15x2) = 0 Solving -54 + -27x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + -9x + 5x2) = 0 Factor a trinomial. 3((-6 + -5x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2Subproblem 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 = {-1.2, 3}
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