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Simplifying 12 = 18x2 + -84x + 102 Reorder the terms: 12 = 102 + -84x + 18x2 Solving 12 = 102 + -84x + 18x2 Solving for variable 'x'. Combine like terms: 12 + -102 = -90 -90 + 84x + -18x2 = 102 + -84x + 18x2 + -102 + 84x + -18x2 Reorder the terms: -90 + 84x + -18x2 = 102 + -102 + -84x + 84x + 18x2 + -18x2 Combine like terms: 102 + -102 = 0 -90 + 84x + -18x2 = 0 + -84x + 84x + 18x2 + -18x2 -90 + 84x + -18x2 = -84x + 84x + 18x2 + -18x2 Combine like terms: -84x + 84x = 0 -90 + 84x + -18x2 = 0 + 18x2 + -18x2 -90 + 84x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -90 + 84x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + 14x + -3x2) = 0 Factor a trinomial. 6((-3 + x)(5 + -3x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {3, 1.666666667}
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