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Simplifying 12x + -27 = x2 + -4x + -12 Reorder the terms: -27 + 12x = x2 + -4x + -12 Reorder the terms: -27 + 12x = -12 + -4x + x2 Solving -27 + 12x = -12 + -4x + x2 Solving for variable 'x'. Reorder the terms: -27 + 12 + 12x + 4x + -1x2 = -12 + -4x + x2 + 12 + 4x + -1x2 Combine like terms: -27 + 12 = -15 -15 + 12x + 4x + -1x2 = -12 + -4x + x2 + 12 + 4x + -1x2 Combine like terms: 12x + 4x = 16x -15 + 16x + -1x2 = -12 + -4x + x2 + 12 + 4x + -1x2 Reorder the terms: -15 + 16x + -1x2 = -12 + 12 + -4x + 4x + x2 + -1x2 Combine like terms: -12 + 12 = 0 -15 + 16x + -1x2 = 0 + -4x + 4x + x2 + -1x2 -15 + 16x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -15 + 16x + -1x2 = 0 + x2 + -1x2 -15 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + 16x + -1x2 = 0 Factor a trinomial. (-15 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-15 + x)' equal to zero and attempt to solve: Simplifying -15 + x = 0 Solving -15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + x = 0 + 15 x = 0 + 15 Combine like terms: 0 + 15 = 15 x = 15 Simplifying x = 15Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {15, 1}
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