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Simplifying 0 = 3x3 + -2x2 + -8x Reorder the terms: 0 = -8x + -2x2 + 3x3 Solving 0 = -8x + -2x2 + 3x3 Solving for variable 'x'. Remove the zero: 8x + 2x2 + -3x3 = -8x + -2x2 + 3x3 + 8x + 2x2 + -3x3 Reorder the terms: 8x + 2x2 + -3x3 = -8x + 8x + -2x2 + 2x2 + 3x3 + -3x3 Combine like terms: -8x + 8x = 0 8x + 2x2 + -3x3 = 0 + -2x2 + 2x2 + 3x3 + -3x3 8x + 2x2 + -3x3 = -2x2 + 2x2 + 3x3 + -3x3 Combine like terms: -2x2 + 2x2 = 0 8x + 2x2 + -3x3 = 0 + 3x3 + -3x3 8x + 2x2 + -3x3 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 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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