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