3mn(4m+8N)=

Solution for 3mn(4m+8N)= equation:

Simplifying
3mn(4m + 8N) = 0

Reorder the terms:
3mn(8N + 4m) = 0
(8N * 3mn + 4m * 3mn) = 0
(24mnN + 12m2n) = 0

Solving
24mnN + 12m2n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '12mn'.
12mn(2N + m) = 0

Ignore the factor 12.
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 '(2N + m)' equal to zero and attempt to solve:

Simplifying
2N + m = 0

Solving
2N + m = 0

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

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

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

Simplifying
m = -2N
Solution
m = {-2N}