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Simplifying 8x + 12 = x2 + 6x + 9 Reorder the terms: 12 + 8x = x2 + 6x + 9 Reorder the terms: 12 + 8x = 9 + 6x + x2 Solving 12 + 8x = 9 + 6x + x2 Solving for variable 'x'. Reorder the terms: 12 + -9 + 8x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Combine like terms: 12 + -9 = 3 3 + 8x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Combine like terms: 8x + -6x = 2x 3 + 2x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Reorder the terms: 3 + 2x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 3 + 2x + -1x2 = 0 + 6x + -6x + x2 + -1x2 3 + 2x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 3 + 2x + -1x2 = 0 + x2 + -1x2 3 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + 2x + -1x2 = 0 Factor a trinomial. (3 + -1x)(1 + x) = 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 '(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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