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Simplifying 4x3 + -1x2 + -2x + 2 = 3x3 + -2(x2 + -1) Reorder the terms: 2 + -2x + -1x2 + 4x3 = 3x3 + -2(x2 + -1) Reorder the terms: 2 + -2x + -1x2 + 4x3 = 3x3 + -2(-1 + x2) 2 + -2x + -1x2 + 4x3 = 3x3 + (-1 * -2 + x2 * -2) 2 + -2x + -1x2 + 4x3 = 3x3 + (2 + -2x2) Reorder the terms: 2 + -2x + -1x2 + 4x3 = 2 + -2x2 + 3x3 Add '-2' to each side of the equation. 2 + -2x + -1x2 + -2 + 4x3 = 2 + -2x2 + -2 + 3x3 Reorder the terms: 2 + -2 + -2x + -1x2 + 4x3 = 2 + -2x2 + -2 + 3x3 Combine like terms: 2 + -2 = 0 0 + -2x + -1x2 + 4x3 = 2 + -2x2 + -2 + 3x3 -2x + -1x2 + 4x3 = 2 + -2x2 + -2 + 3x3 Reorder the terms: -2x + -1x2 + 4x3 = 2 + -2 + -2x2 + 3x3 Combine like terms: 2 + -2 = 0 -2x + -1x2 + 4x3 = 0 + -2x2 + 3x3 -2x + -1x2 + 4x3 = -2x2 + 3x3 Solving -2x + -1x2 + 4x3 = -2x2 + 3x3 Solving for variable 'x'. Reorder the terms: -2x + -1x2 + 2x2 + 4x3 + -3x3 = -2x2 + 3x3 + 2x2 + -3x3 Combine like terms: -1x2 + 2x2 = 1x2 -2x + 1x2 + 4x3 + -3x3 = -2x2 + 3x3 + 2x2 + -3x3 Combine like terms: 4x3 + -3x3 = 1x3 -2x + 1x2 + 1x3 = -2x2 + 3x3 + 2x2 + -3x3 Reorder the terms: -2x + 1x2 + 1x3 = -2x2 + 2x2 + 3x3 + -3x3 Combine like terms: -2x2 + 2x2 = 0 -2x + 1x2 + 1x3 = 0 + 3x3 + -3x3 -2x + 1x2 + 1x3 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 -2x + 1x2 + 1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + x + x2) = 0 Factor a trinomial. x((-2 + -1x)(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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 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, -2, 1}
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