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Simplifying 2x2 + -1(x + 2)(x + -3) + -12 = 0 Reorder the terms: 2x2 + -1(2 + x)(x + -3) + -12 = 0 Reorder the terms: 2x2 + -1(2 + x)(-3 + x) + -12 = 0 Multiply (2 + x) * (-3 + x) 2x2 + -1(2(-3 + x) + x(-3 + x)) + -12 = 0 2x2 + -1((-3 * 2 + x * 2) + x(-3 + x)) + -12 = 0 2x2 + -1((-6 + 2x) + x(-3 + x)) + -12 = 0 2x2 + -1(-6 + 2x + (-3 * x + x * x)) + -12 = 0 2x2 + -1(-6 + 2x + (-3x + x2)) + -12 = 0 Combine like terms: 2x + -3x = -1x 2x2 + -1(-6 + -1x + x2) + -12 = 0 2x2 + (-6 * -1 + -1x * -1 + x2 * -1) + -12 = 0 2x2 + (6 + 1x + -1x2) + -12 = 0 Reorder the terms: 6 + -12 + 1x + 2x2 + -1x2 = 0 Combine like terms: 6 + -12 = -6 -6 + 1x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -6 + 1x + 1x2 = 0 Solving -6 + 1x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -1x)(2 + -1x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-3, 2}
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