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Simplifying 0 = 36x + -12x2 + x3 Solving 0 = 36x + -12x2 + x3 Solving for variable 'x'. Remove the zero: -36x + 12x2 + -1x3 = 36x + -12x2 + x3 + -36x + 12x2 + -1x3 Reorder the terms: -36x + 12x2 + -1x3 = 36x + -36x + -12x2 + 12x2 + x3 + -1x3 Combine like terms: 36x + -36x = 0 -36x + 12x2 + -1x3 = 0 + -12x2 + 12x2 + x3 + -1x3 -36x + 12x2 + -1x3 = -12x2 + 12x2 + x3 + -1x3 Combine like terms: -12x2 + 12x2 = 0 -36x + 12x2 + -1x3 = 0 + x3 + -1x3 -36x + 12x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -36x + 12x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + 12x + -1x2) = 0 Factor a trinomial. x((-6 + x)(6 + -1x)) = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, 6, 6}
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