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Simplifying x3 + -3x2 + x + -5 = -1x2 + 4x + -5 Reorder the terms: -5 + x + -3x2 + x3 = -1x2 + 4x + -5 Reorder the terms: -5 + x + -3x2 + x3 = -5 + 4x + -1x2 Add '5' to each side of the equation. -5 + x + -3x2 + 5 + x3 = -5 + 4x + 5 + -1x2 Reorder the terms: -5 + 5 + x + -3x2 + x3 = -5 + 4x + 5 + -1x2 Combine like terms: -5 + 5 = 0 0 + x + -3x2 + x3 = -5 + 4x + 5 + -1x2 x + -3x2 + x3 = -5 + 4x + 5 + -1x2 Reorder the terms: x + -3x2 + x3 = -5 + 5 + 4x + -1x2 Combine like terms: -5 + 5 = 0 x + -3x2 + x3 = 0 + 4x + -1x2 x + -3x2 + x3 = 4x + -1x2 Solving x + -3x2 + x3 = 4x + -1x2 Solving for variable 'x'. Reorder the terms: x + -4x + -3x2 + x2 + x3 = 4x + -1x2 + -4x + x2 Combine like terms: x + -4x = -3x -3x + -3x2 + x2 + x3 = 4x + -1x2 + -4x + x2 Combine like terms: -3x2 + x2 = -2x2 -3x + -2x2 + x3 = 4x + -1x2 + -4x + x2 Reorder the terms: -3x + -2x2 + x3 = 4x + -4x + -1x2 + x2 Combine like terms: 4x + -4x = 0 -3x + -2x2 + x3 = 0 + -1x2 + x2 -3x + -2x2 + x3 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -3x + -2x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + -2x + 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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