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Simplifying 6x + 31 = 9x2 + -12x + 4 Reorder the terms: 31 + 6x = 9x2 + -12x + 4 Reorder the terms: 31 + 6x = 4 + -12x + 9x2 Solving 31 + 6x = 4 + -12x + 9x2 Solving for variable 'x'. Reorder the terms: 31 + -4 + 6x + 12x + -9x2 = 4 + -12x + 9x2 + -4 + 12x + -9x2 Combine like terms: 31 + -4 = 27 27 + 6x + 12x + -9x2 = 4 + -12x + 9x2 + -4 + 12x + -9x2 Combine like terms: 6x + 12x = 18x 27 + 18x + -9x2 = 4 + -12x + 9x2 + -4 + 12x + -9x2 Reorder the terms: 27 + 18x + -9x2 = 4 + -4 + -12x + 12x + 9x2 + -9x2 Combine like terms: 4 + -4 = 0 27 + 18x + -9x2 = 0 + -12x + 12x + 9x2 + -9x2 27 + 18x + -9x2 = -12x + 12x + 9x2 + -9x2 Combine like terms: -12x + 12x = 0 27 + 18x + -9x2 = 0 + 9x2 + -9x2 27 + 18x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 27 + 18x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(3 + 2x + -1x2) = 0 Factor a trinomial. 9((3 + -1x)(1 + x)) = 0 Ignore the factor 9.Subproblem 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {3, -1}
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