5m^2n-mn+3m^2n=2mn

Solution for 5m^2n-mn+3m^2n=2mn equation:

Simplifying
5m2n + -1mn + 3m2n = 2mn

Reorder the terms:
-1mn + 5m2n + 3m2n = 2mn

Combine like terms: 5m2n + 3m2n = 8m2n
-1mn + 8m2n = 2mn

Solving
-1mn + 8m2n = 2mn

Solving for variable 'm'.

Reorder the terms:
-1mn + -2mn + 8m2n = 2mn + -2mn

Combine like terms: -1mn + -2mn = -3mn
-3mn + 8m2n = 2mn + -2mn

Combine like terms: 2mn + -2mn = 0
-3mn + 8m2n = 0

Factor out the Greatest Common Factor (GCF), 'mn'.
mn(-3 + 8m) = 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 '(-3 + 8m)' equal to zero and attempt to solve:

Simplifying
-3 + 8m = 0

Solving
-3 + 8m = 0

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

Add '3' to each side of the equation.
-3 + 3 + 8m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 8m = 0 + 3
8m = 0 + 3

Combine like terms: 0 + 3 = 3
8m = 3

Divide each side by '8'.
m = 0.375

Simplifying
m = 0.375
Solution
m = {0.375}