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Simplifying 3x2 + -1x = x2 + -5x + 6 Reorder the terms: -1x + 3x2 = x2 + -5x + 6 Reorder the terms: -1x + 3x2 = 6 + -5x + x2 Solving -1x + 3x2 = 6 + -5x + x2 Solving for variable 'x'. Reorder the terms: -6 + -1x + 5x + 3x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2 Combine like terms: -1x + 5x = 4x -6 + 4x + 3x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -6 + 4x + 2x2 = 6 + -5x + x2 + -6 + 5x + -1x2 Reorder the terms: -6 + 4x + 2x2 = 6 + -6 + -5x + 5x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -6 + 4x + 2x2 = 0 + -5x + 5x + x2 + -1x2 -6 + 4x + 2x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 -6 + 4x + 2x2 = 0 + x2 + -1x2 -6 + 4x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 2x + x2) = 0 Factor a trinomial. 2((-3 + -1x)(1 + -1x)) = 0 Ignore the factor 2.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 + -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 = {-3, 1}
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