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Simplifying 2x3 + -4x2 + 6x + -3 + x3 + 6x2 + -8x + 12 + -3x3 + 2x2 + -4x + -7 = 0 Reorder the terms: -3 + 12 + -7 + 6x + -8x + -4x + -4x2 + 6x2 + 2x2 + 2x3 + x3 + -3x3 = 0 Combine like terms: -3 + 12 = 9 9 + -7 + 6x + -8x + -4x + -4x2 + 6x2 + 2x2 + 2x3 + x3 + -3x3 = 0 Combine like terms: 9 + -7 = 2 2 + 6x + -8x + -4x + -4x2 + 6x2 + 2x2 + 2x3 + x3 + -3x3 = 0 Combine like terms: 6x + -8x = -2x 2 + -2x + -4x + -4x2 + 6x2 + 2x2 + 2x3 + x3 + -3x3 = 0 Combine like terms: -2x + -4x = -6x 2 + -6x + -4x2 + 6x2 + 2x2 + 2x3 + x3 + -3x3 = 0 Combine like terms: -4x2 + 6x2 = 2x2 2 + -6x + 2x2 + 2x2 + 2x3 + x3 + -3x3 = 0 Combine like terms: 2x2 + 2x2 = 4x2 2 + -6x + 4x2 + 2x3 + x3 + -3x3 = 0 Combine like terms: 2x3 + x3 = 3x3 2 + -6x + 4x2 + 3x3 + -3x3 = 0 Combine like terms: 3x3 + -3x3 = 0 2 + -6x + 4x2 + 0 = 0 2 + -6x + 4x2 = 0 Solving 2 + -6x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -3x + 2x2) = 0 Factor a trinomial. 2((1 + -2x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 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 = {0.5, 1}
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