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Simplifying (x + 3)(6x + -9) = 0 Reorder the terms: (3 + x)(6x + -9) = 0 Reorder the terms: (3 + x)(-9 + 6x) = 0 Multiply (3 + x) * (-9 + 6x) (3(-9 + 6x) + x(-9 + 6x)) = 0 ((-9 * 3 + 6x * 3) + x(-9 + 6x)) = 0 ((-27 + 18x) + x(-9 + 6x)) = 0 (-27 + 18x + (-9 * x + 6x * x)) = 0 (-27 + 18x + (-9x + 6x2)) = 0 Combine like terms: 18x + -9x = 9x (-27 + 9x + 6x2) = 0 Solving -27 + 9x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 3x + 2x2) = 0 Factor a trinomial. 3((-3 + -1x)(3 + -2x)) = 0 Ignore the factor 3.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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-3, 1.5}
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