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Simplifying 32x2 = 12x + -12x3 Solving 32x2 = 12x + -12x3 Solving for variable 'x'. Reorder the terms: -12x + 32x2 + 12x3 = 12x + -12x3 + -12x + 12x3 Reorder the terms: -12x + 32x2 + 12x3 = 12x + -12x + -12x3 + 12x3 Combine like terms: 12x + -12x = 0 -12x + 32x2 + 12x3 = 0 + -12x3 + 12x3 -12x + 32x2 + 12x3 = -12x3 + 12x3 Combine like terms: -12x3 + 12x3 = 0 -12x + 32x2 + 12x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-3 + 8x + 3x2) = 0 Factor a trinomial. 4x((-3 + -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 '(-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 = -3Subproblem 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, -3, 0.3333333333}
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