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Simplifying 0 = 12x3 + -20x2 + -8x Reorder the terms: 0 = -8x + -20x2 + 12x3 Solving 0 = -8x + -20x2 + 12x3 Solving for variable 'x'. Remove the zero: 8x + 20x2 + -12x3 = -8x + -20x2 + 12x3 + 8x + 20x2 + -12x3 Reorder the terms: 8x + 20x2 + -12x3 = -8x + 8x + -20x2 + 20x2 + 12x3 + -12x3 Combine like terms: -8x + 8x = 0 8x + 20x2 + -12x3 = 0 + -20x2 + 20x2 + 12x3 + -12x3 8x + 20x2 + -12x3 = -20x2 + 20x2 + 12x3 + -12x3 Combine like terms: -20x2 + 20x2 = 0 8x + 20x2 + -12x3 = 0 + 12x3 + -12x3 8x + 20x2 + -12x3 = 12x3 + -12x3 Combine like terms: 12x3 + -12x3 = 0 8x + 20x2 + -12x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(2 + 5x + -3x2) = 0 Factor a trinomial. 4x((2 + -1x)(1 + 3x)) = 0 Ignore the factor 4.Subproblem 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 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {0, 2, -0.3333333333}
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