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Simplifying x2 + -1 = x3 + -3x2 + 3x + -1 Reorder the terms: -1 + x2 = x3 + -3x2 + 3x + -1 Reorder the terms: -1 + x2 = -1 + 3x + -3x2 + x3 Add '1' to each side of the equation. -1 + 1 + x2 = -1 + 3x + -3x2 + 1 + x3 Combine like terms: -1 + 1 = 0 0 + x2 = -1 + 3x + -3x2 + 1 + x3 x2 = -1 + 3x + -3x2 + 1 + x3 Reorder the terms: x2 = -1 + 1 + 3x + -3x2 + x3 Combine like terms: -1 + 1 = 0 x2 = 0 + 3x + -3x2 + x3 x2 = 3x + -3x2 + x3 Solving x2 = 3x + -3x2 + x3 Solving for variable 'x'. Reorder the terms: -3x + x2 + 3x2 + -1x3 = 3x + -3x2 + x3 + -3x + 3x2 + -1x3 Combine like terms: x2 + 3x2 = 4x2 -3x + 4x2 + -1x3 = 3x + -3x2 + x3 + -3x + 3x2 + -1x3 Reorder the terms: -3x + 4x2 + -1x3 = 3x + -3x + -3x2 + 3x2 + x3 + -1x3 Combine like terms: 3x + -3x = 0 -3x + 4x2 + -1x3 = 0 + -3x2 + 3x2 + x3 + -1x3 -3x + 4x2 + -1x3 = -3x2 + 3x2 + x3 + -1x3 Combine like terms: -3x2 + 3x2 = 0 -3x + 4x2 + -1x3 = 0 + x3 + -1x3 -3x + 4x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -3x + 4x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + 4x + -1x2) = 0 Factor a trinomial. x((-3 + x)(1 + -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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 3
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, 3, 1}
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