nm(m-3n)(m+3n)=0

Solution for nm(m-3n)(m+3n)=0 equation:

Simplifying
nm(m + -3n)(m + 3n) = 0

Multiply (m + -3n) * (m + 3n)
mn(m(m + 3n) + -3n * (m + 3n)) = 0
mn((m * m + 3n * m) + -3n * (m + 3n)) = 0

Reorder the terms:
mn((3mn + m2) + -3n * (m + 3n)) = 0
mn((3mn + m2) + -3n * (m + 3n)) = 0
mn(3mn + m2 + (m * -3n + 3n * -3n)) = 0
mn(3mn + m2 + (-3mn + -9n2)) = 0

Reorder the terms:
mn(3mn + -3mn + m2 + -9n2) = 0

Combine like terms: 3mn + -3mn = 0
mn(0 + m2 + -9n2) = 0
mn(m2 + -9n2) = 0
(m2 * mn + -9n2 * mn) = 0

Reorder the terms:
(-9mn3 + m3n) = 0
(-9mn3 + m3n) = 0

Solving
-9mn3 + m3n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'mn'.
mn(-9n2 + m2) = 0

Factor a difference between two squares.
mn((3n + m)(-3n + m)) = 0

Subproblem 1
Set the factor 'mn' equal to zero and attempt to solve:

Simplifying
mn = 0

Solving
mn = 0

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

Simplifying
mn = 0

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 '(3n + m)' equal to zero and attempt to solve:

Simplifying
3n + m = 0

Reorder the terms:
m + 3n = 0

Solving
m + 3n = 0

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

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

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

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

Simplifying
-3n + m = 0

Reorder the terms:
m + -3n = 0

Solving
m + -3n = 0

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

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

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

Simplifying
m = 3n
Solution
m = {-3n, 3n}