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Simplifying x2 + 4x + 6 = 2x2 + 5x + -6 Reorder the terms: 6 + 4x + x2 = 2x2 + 5x + -6 Reorder the terms: 6 + 4x + x2 = -6 + 5x + 2x2 Solving 6 + 4x + x2 = -6 + 5x + 2x2 Solving for variable 'x'. Reorder the terms: 6 + 6 + 4x + -5x + x2 + -2x2 = -6 + 5x + 2x2 + 6 + -5x + -2x2 Combine like terms: 6 + 6 = 12 12 + 4x + -5x + x2 + -2x2 = -6 + 5x + 2x2 + 6 + -5x + -2x2 Combine like terms: 4x + -5x = -1x 12 + -1x + x2 + -2x2 = -6 + 5x + 2x2 + 6 + -5x + -2x2 Combine like terms: x2 + -2x2 = -1x2 12 + -1x + -1x2 = -6 + 5x + 2x2 + 6 + -5x + -2x2 Reorder the terms: 12 + -1x + -1x2 = -6 + 6 + 5x + -5x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 12 + -1x + -1x2 = 0 + 5x + -5x + 2x2 + -2x2 12 + -1x + -1x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 12 + -1x + -1x2 = 0 + 2x2 + -2x2 12 + -1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12 + -1x + -1x2 = 0 Factor a trinomial. (3 + -1x)(4 + 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {3, -4}
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