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Simplifying 0 = 2x2 + 11x + 12 Reorder the terms: 0 = 12 + 11x + 2x2 Solving 0 = 12 + 11x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -11x + -2x2 = 12 + 11x + 2x2 + -12 + -11x + -2x2 Reorder the terms: -12 + -11x + -2x2 = 12 + -12 + 11x + -11x + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -12 + -11x + -2x2 = 0 + 11x + -11x + 2x2 + -2x2 -12 + -11x + -2x2 = 11x + -11x + 2x2 + -2x2 Combine like terms: 11x + -11x = 0 -12 + -11x + -2x2 = 0 + 2x2 + -2x2 -12 + -11x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + -11x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 11x + 2x2) = 0 Factor a trinomial. -1((4 + x)(3 + 2x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 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 = {-4, -1.5}
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