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Simplifying 0 = 12x3 + -24x2 + 12x Reorder the terms: 0 = 12x + -24x2 + 12x3 Solving 0 = 12x + -24x2 + 12x3 Solving for variable 'x'. Remove the zero: -12x + 24x2 + -12x3 = 12x + -24x2 + 12x3 + -12x + 24x2 + -12x3 Reorder the terms: -12x + 24x2 + -12x3 = 12x + -12x + -24x2 + 24x2 + 12x3 + -12x3 Combine like terms: 12x + -12x = 0 -12x + 24x2 + -12x3 = 0 + -24x2 + 24x2 + 12x3 + -12x3 -12x + 24x2 + -12x3 = -24x2 + 24x2 + 12x3 + -12x3 Combine like terms: -24x2 + 24x2 = 0 -12x + 24x2 + -12x3 = 0 + 12x3 + -12x3 -12x + 24x2 + -12x3 = 12x3 + -12x3 Combine like terms: 12x3 + -12x3 = 0 -12x + 24x2 + -12x3 = 0 Factor out the Greatest Common Factor (GCF), '12x'. 12x(-1 + 2x + -1x2) = 0 Factor a trinomial. 12x((-1 + x)(1 + -1x)) = 0 Ignore the factor 12.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, 1, 1}
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