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Simplifying 2x + -3 = x2 + -6x + 9 Reorder the terms: -3 + 2x = x2 + -6x + 9 Reorder the terms: -3 + 2x = 9 + -6x + x2 Solving -3 + 2x = 9 + -6x + x2 Solving for variable 'x'. Reorder the terms: -3 + -9 + 2x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: -3 + -9 = -12 -12 + 2x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: 2x + 6x = 8x -12 + 8x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Reorder the terms: -12 + 8x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -12 + 8x + -1x2 = 0 + -6x + 6x + x2 + -1x2 -12 + 8x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -12 + 8x + -1x2 = 0 + x2 + -1x2 -12 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + 8x + -1x2 = 0 Factor a trinomial. (-6 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 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 = {6, 2}
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