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Simplifying 0 = -2x3 + 24x2 + -72x Reorder the terms: 0 = -72x + 24x2 + -2x3 Solving 0 = -72x + 24x2 + -2x3 Solving for variable 'x'. Remove the zero: 72x + -24x2 + 2x3 = -72x + 24x2 + -2x3 + 72x + -24x2 + 2x3 Reorder the terms: 72x + -24x2 + 2x3 = -72x + 72x + 24x2 + -24x2 + -2x3 + 2x3 Combine like terms: -72x + 72x = 0 72x + -24x2 + 2x3 = 0 + 24x2 + -24x2 + -2x3 + 2x3 72x + -24x2 + 2x3 = 24x2 + -24x2 + -2x3 + 2x3 Combine like terms: 24x2 + -24x2 = 0 72x + -24x2 + 2x3 = 0 + -2x3 + 2x3 72x + -24x2 + 2x3 = -2x3 + 2x3 Combine like terms: -2x3 + 2x3 = 0 72x + -24x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(36 + -12x + x2) = 0 Factor a trinomial. 2x((6 + -1x)(6 + -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 '(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 = 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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