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Simplifying 2m3 + 12m + -10m2 = 14m2 + -42m Reorder the terms: 12m + -10m2 + 2m3 = 14m2 + -42m Reorder the terms: 12m + -10m2 + 2m3 = -42m + 14m2 Solving 12m + -10m2 + 2m3 = -42m + 14m2 Solving for variable 'm'. Reorder the terms: 12m + 42m + -10m2 + -14m2 + 2m3 = -42m + 14m2 + 42m + -14m2 Combine like terms: 12m + 42m = 54m 54m + -10m2 + -14m2 + 2m3 = -42m + 14m2 + 42m + -14m2 Combine like terms: -10m2 + -14m2 = -24m2 54m + -24m2 + 2m3 = -42m + 14m2 + 42m + -14m2 Reorder the terms: 54m + -24m2 + 2m3 = -42m + 42m + 14m2 + -14m2 Combine like terms: -42m + 42m = 0 54m + -24m2 + 2m3 = 0 + 14m2 + -14m2 54m + -24m2 + 2m3 = 14m2 + -14m2 Combine like terms: 14m2 + -14m2 = 0 54m + -24m2 + 2m3 = 0 Factor out the Greatest Common Factor (GCF), '2m'. 2m(27 + -12m + m2) = 0 Factor a trinomial. 2m((3 + -1m)(9 + -1m)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(3 + -1m)' equal to zero and attempt to solve: Simplifying 3 + -1m = 0 Solving 3 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1m = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1m = 0 + -3 -1m = 0 + -3 Combine like terms: 0 + -3 = -3 -1m = -3 Divide each side by '-1'. m = 3 Simplifying m = 3Subproblem 3
Set the factor '(9 + -1m)' equal to zero and attempt to solve: Simplifying 9 + -1m = 0 Solving 9 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1m = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1m = 0 + -9 -1m = 0 + -9 Combine like terms: 0 + -9 = -9 -1m = -9 Divide each side by '-1'. m = 9 Simplifying m = 9Solution
m = {0, 3, 9}
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