6m^3-9m^2n-15n^2m=0

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Solution for 6m^3-9m^2n-15n^2m=0 equation: 


Simplifying
6m3 + -9m2n + -15n2m = 0

Reorder the terms:
-15mn2 + -9m2n + 6m3 = 0

Solving
-15mn2 + -9m2n + 6m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3m'.
3m(-5n2 + -3mn + 2m2) = 0

Factor a trinomial.
3m((-1n + -1m)(5n + -2m)) = 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 '(-1n + -1m)' equal to zero and attempt to solve:

Simplifying
-1n + -1m = 0

Reorder the terms:
-1m + -1n = 0

Solving
-1m + -1n = 0

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

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

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

Divide each side by '-1'.
m = -1n

Simplifying
m = -1n

Subproblem 3
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
Solution
m = {0, -1n, 2.5n}

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