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Simplifying 12x2 + 27x + -39 = 0 Reorder the terms: -39 + 27x + 12x2 = 0 Solving -39 + 27x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + 9x + 4x2) = 0 Factor a trinomial. 3((-13 + -4x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + -4x)' equal to zero and attempt to solve: Simplifying -13 + -4x = 0 Solving -13 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -4x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4x = 0 + 13 -4x = 0 + 13 Combine like terms: 0 + 13 = 13 -4x = 13 Divide each side by '-4'. x = -3.25 Simplifying x = -3.25Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-3.25, 1}
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