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Simplifying 0 = 2x2 + -5x + -12 Reorder the terms: 0 = -12 + -5x + 2x2 Solving 0 = -12 + -5x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + 5x + -2x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2 Reorder the terms: 12 + 5x + -2x2 = -12 + 12 + -5x + 5x + 2x2 + -2x2 Combine like terms: -12 + 12 = 0 12 + 5x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2 12 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 12 + 5x + -2x2 = 0 + 2x2 + -2x2 12 + 5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12 + 5x + -2x2 = 0 Factor a trinomial. (4 + -1x)(3 + 2x) = 0Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. 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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