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Simplifying 2x2 + -5x + 6 = -2x2 + -1x + 30 Reorder the terms: 6 + -5x + 2x2 = -2x2 + -1x + 30 Reorder the terms: 6 + -5x + 2x2 = 30 + -1x + -2x2 Solving 6 + -5x + 2x2 = 30 + -1x + -2x2 Solving for variable 'x'. Reorder the terms: 6 + -30 + -5x + x + 2x2 + 2x2 = 30 + -1x + -2x2 + -30 + x + 2x2 Combine like terms: 6 + -30 = -24 -24 + -5x + x + 2x2 + 2x2 = 30 + -1x + -2x2 + -30 + x + 2x2 Combine like terms: -5x + x = -4x -24 + -4x + 2x2 + 2x2 = 30 + -1x + -2x2 + -30 + x + 2x2 Combine like terms: 2x2 + 2x2 = 4x2 -24 + -4x + 4x2 = 30 + -1x + -2x2 + -30 + x + 2x2 Reorder the terms: -24 + -4x + 4x2 = 30 + -30 + -1x + x + -2x2 + 2x2 Combine like terms: 30 + -30 = 0 -24 + -4x + 4x2 = 0 + -1x + x + -2x2 + 2x2 -24 + -4x + 4x2 = -1x + x + -2x2 + 2x2 Combine like terms: -1x + x = 0 -24 + -4x + 4x2 = 0 + -2x2 + 2x2 -24 + -4x + 4x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -24 + -4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -1x + x2) = 0 Factor a trinomial. 4((-2 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
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 = -2Subproblem 2
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 = 3Solution
x = {-2, 3}
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