18m^3+39m^2n-15mn^2=0

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Solution for 18m^3+39m^2n-15mn^2=0 equation: 


Simplifying
18m3 + 39m2n + -15mn2 = 0

Reorder the terms:
-15mn2 + 39m2n + 18m3 = 0

Solving
-15mn2 + 39m2n + 18m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3m'.
3m(-5n2 + 13mn + 6m2) = 0

Factor a trinomial.
3m((-5n + -2m)(n + -3m)) = 0

Ignore the factor 3.

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 = 0

Subproblem 2
Set the factor '(-5n + -2m)' equal to zero and attempt to solve:

Simplifying
-5n + -2m = 0

Reorder the terms:
-2m + -5n = 0

Solving
-2m + -5n = 0

Move all terms containing m to the left, all other terms to the right.

Add '5n' to each side of the equation.
-2m + -5n + 5n = 0 + 5n

Combine like terms: -5n + 5n = 0
-2m + 0 = 0 + 5n
-2m = 0 + 5n
Remove the zero:
-2m = 5n

Divide each side by '-2'.
m = -2.5n

Simplifying
m = -2.5n

Subproblem 3
Set the factor '(n + -3m)' equal to zero and attempt to solve:

Simplifying
n + -3m = 0

Reorder the terms:
-3m + n = 0

Solving
-3m + n = 0

Move all terms containing m to the left, all other terms to the right.

Add '-1n' to each side of the equation.
-3m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
-3m + 0 = 0 + -1n
-3m = 0 + -1n
Remove the zero:
-3m = -1n

Divide each side by '-3'.
m = 0.3333333333n

Simplifying
m = 0.3333333333n
Solution
m = {0, -2.5n, 0.3333333333n}

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