6mn(m+n)=

Solution for 6mn(m+n)= equation:

Simplifying
6mn(m + n) = 0
(m * 6mn + n * 6mn) = 0

Reorder the terms:
(6mn2 + 6m2n) = 0
(6mn2 + 6m2n) = 0

Solving
6mn2 + 6m2n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '6mn'.
6mn(n + m) = 0

Ignore the factor 6.
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 '(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}