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Simplifying 0 = (12x2) + 6x + -18 Reorder the terms: 0 = -18 + 6x + (12x2) Solving 0 = -18 + 6x + (12x2) Solving for variable 'x'. Combine like terms: 0 + 18 = 18 18 + -6x + (-12x2) = -18 + 6x + (12x2) + 18 + -6x + (-12x2) Reorder the terms: 18 + -6x + (-12x2) = -18 + 18 + 6x + -6x + (12x2) + (-12x2) Combine like terms: -18 + 18 = 0 18 + -6x + (-12x2) = 0 + 6x + -6x + (12x2) + (-12x2) 18 + -6x + (-12x2) = 6x + -6x + (12x2) + (-12x2) Combine like terms: 6x + -6x = 0 18 + -6x + (-12x2) = 0 + (12x2) + (-12x2) 18 + -6x + (-12x2) = (12x2) + (-12x2) Combine like terms: (12x2) + (-12x2) = 0 18 + -6x + (-12x2) = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3 + -1x + (-2x2)) = 0 Factor a trinomial. 6((1 + -1x)(3 + 2x)) = 0 Ignore the factor 6.Subproblem 1
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 = 1Subproblem 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 = {1, -1.5}
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