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Simplifying 4x + -1x2 + 6 = 12x + x2 + -4 Reorder the terms: 6 + 4x + -1x2 = 12x + x2 + -4 Reorder the terms: 6 + 4x + -1x2 = -4 + 12x + x2 Solving 6 + 4x + -1x2 = -4 + 12x + x2 Solving for variable 'x'. Reorder the terms: 6 + 4 + 4x + -12x + -1x2 + -1x2 = -4 + 12x + x2 + 4 + -12x + -1x2 Combine like terms: 6 + 4 = 10 10 + 4x + -12x + -1x2 + -1x2 = -4 + 12x + x2 + 4 + -12x + -1x2 Combine like terms: 4x + -12x = -8x 10 + -8x + -1x2 + -1x2 = -4 + 12x + x2 + 4 + -12x + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 10 + -8x + -2x2 = -4 + 12x + x2 + 4 + -12x + -1x2 Reorder the terms: 10 + -8x + -2x2 = -4 + 4 + 12x + -12x + x2 + -1x2 Combine like terms: -4 + 4 = 0 10 + -8x + -2x2 = 0 + 12x + -12x + x2 + -1x2 10 + -8x + -2x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 10 + -8x + -2x2 = 0 + x2 + -1x2 10 + -8x + -2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -4x + -1x2) = 0 Factor a trinomial. 2((1 + -1x)(5 + x)) = 0 Ignore the factor 2.Subproblem 1
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 = 1Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {1, -5}
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