4m^2n(-3mn)(m+n)=0

Solution for 4m^2n(-3mn)(m+n)=0 equation:

Simplifying
4m2n(-3mn)(m + n) = 0

Remove parenthesis around (-3mn)
4m2n * -3mn(m + n) = 0

Reorder the terms for easier multiplication:
4 * -3m2n * mn(m + n) = 0

Multiply 4 * -3
-12m2n * mn(m + n) = 0

Multiply m2n * mn
-12m3n2(m + n) = 0
(m * -12m3n2 + n * -12m3n2) = 0

Reorder the terms:
(-12m3n3 + -12m4n2) = 0
(-12m3n3 + -12m4n2) = 0

Solving
-12m3n3 + -12m4n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '-12m3n2'.
-12m3n2(n + m) = 0

Ignore the factor -12.
Subproblem 1
Set the factor 'm3n2' equal to zero and attempt to solve:

Simplifying
m3n2 = 0

Solving
m3n2 = 0

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

Simplifying
m3n2 = 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 '(n + m)' equal to zero and attempt to solve:

Simplifying
n + m = 0

Reorder the terms:
m + n = 0

Solving
m + n = 0

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

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

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

Simplifying
m = -1n
Solution
m = {-1n}