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Simplifying 3x3 = 8x + -2x2 Solving 3x3 = 8x + -2x2 Solving for variable 'x'. Reorder the terms: -8x + 2x2 + 3x3 = 8x + -2x2 + -8x + 2x2 Reorder the terms: -8x + 2x2 + 3x3 = 8x + -8x + -2x2 + 2x2 Combine like terms: 8x + -8x = 0 -8x + 2x2 + 3x3 = 0 + -2x2 + 2x2 -8x + 2x2 + 3x3 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -8x + 2x2 + 3x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + 2x + 3x2) = 0 Factor a trinomial. x((-2 + -1x)(4 + -3x)) = 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 '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {0, -2, 1.333333333}
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