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Simplifying x3 + -2x2 = 2x2 + -3x Reorder the terms: -2x2 + x3 = 2x2 + -3x Reorder the terms: -2x2 + x3 = -3x + 2x2 Solving -2x2 + x3 = -3x + 2x2 Solving for variable 'x'. Reorder the terms: 3x + -2x2 + -2x2 + x3 = -3x + 2x2 + 3x + -2x2 Combine like terms: -2x2 + -2x2 = -4x2 3x + -4x2 + x3 = -3x + 2x2 + 3x + -2x2 Reorder the terms: 3x + -4x2 + x3 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 3x + -4x2 + x3 = 0 + 2x2 + -2x2 3x + -4x2 + x3 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 3x + -4x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(3 + -4x + x2) = 0 Factor a trinomial. x((1 + -1x)(3 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = 1Subproblem 3
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 = 3Solution
x = {0, 1, 3}
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