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Simplifying 12x2 = 32x + -2x3 Solving 12x2 = 32x + -2x3 Solving for variable 'x'. Reorder the terms: -32x + 12x2 + 2x3 = 32x + -2x3 + -32x + 2x3 Reorder the terms: -32x + 12x2 + 2x3 = 32x + -32x + -2x3 + 2x3 Combine like terms: 32x + -32x = 0 -32x + 12x2 + 2x3 = 0 + -2x3 + 2x3 -32x + 12x2 + 2x3 = -2x3 + 2x3 Combine like terms: -2x3 + 2x3 = 0 -32x + 12x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-16 + 6x + x2) = 0 Factor a trinomial. 2x((-8 + -1x)(2 + -1x)) = 0 Ignore the factor 2.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 '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 3
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 = 2Solution
x = {0, -8, 2}
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