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Simplifying 18m2n + 48mn2 + 32n3 = 0 Reorder the terms: 48mn2 + 18m2n + 32n3 = 0 Solving 48mn2 + 18m2n + 32n3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(24mn + 9m2 + 16n2) = 0 Factor a trinomial. 2n((3m + 4n)(3m + 4n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing m to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3m + 4n)' equal to zero and attempt to solve: Simplifying 3m + 4n = 0 Solving 3m + 4n = 0 Move all terms containing m to the left, all other terms to the right. Add '-4n' to each side of the equation. 3m + 4n + -4n = 0 + -4n Combine like terms: 4n + -4n = 0 3m + 0 = 0 + -4n 3m = 0 + -4n Remove the zero: 3m = -4n Divide each side by '3'. m = -1.333333333n Simplifying m = -1.333333333nSubproblem 3
Set the factor '(3m + 4n)' equal to zero and attempt to solve: Simplifying 3m + 4n = 0 Solving 3m + 4n = 0 Move all terms containing m to the left, all other terms to the right. Add '-4n' to each side of the equation. 3m + 4n + -4n = 0 + -4n Combine like terms: 4n + -4n = 0 3m + 0 = 0 + -4n 3m = 0 + -4n Remove the zero: 3m = -4n Divide each side by '3'. m = -1.333333333n Simplifying m = -1.333333333nSolution
m = {-1.333333333n, -1.333333333n}
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