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Simplifying 3x(2x + -3) = 27 Reorder the terms: 3x(-3 + 2x) = 27 (-3 * 3x + 2x * 3x) = 27 (-9x + 6x2) = 27 Solving -9x + 6x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + -9x + 6x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -9x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + -3x + 2x2) = 0 Factor a trinomial. 3((-3 + -2x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = -1.5Subproblem 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 = {-1.5, 3}
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