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

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

Simplifying
5m2n + -1mn + 3m3n = 2mn

Reorder the terms:
-1mn + 5m2n + 3m3n = 2mn

Solving
-1mn + 5m2n + 3m3n = 2mn

Solving for variable 'm'.

Reorder the terms:
-1mn + -2mn + 5m2n + 3m3n = 2mn + -2mn

Combine like terms: -1mn + -2mn = -3mn
-3mn + 5m2n + 3m3n = 2mn + -2mn

Combine like terms: 2mn + -2mn = 0
-3mn + 5m2n + 3m3n = 0

Factor out the Greatest Common Factor (GCF), 'mn'.
mn(-3 + 5m + 3m2) = 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 + 5m + 3m2)' equal to zero and attempt to solve:

Simplifying
-3 + 5m + 3m2 = 0

Solving
-3 + 5m + 3m2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-1 + 1.666666667m + m2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.666666667m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.666666667m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.666666667m + m2 = 0 + 1
1.666666667m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.666666667m + m2 = 1

The m term is 1.666666667m.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667m + 0.6944444447 + m2 = 1 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667m + m2 = 1 + 0.6944444447

Combine like terms: 1 + 0.6944444447 = 1.6944444447
0.6944444447 + 1.666666667m + m2 = 1.6944444447

Factor a perfect square on the left side:
(m + 0.8333333335)(m + 0.8333333335) = 1.6944444447

Calculate the square root of the right side: 1.301708279

Break this problem into two subproblems by setting 
(m + 0.8333333335) equal to 1.301708279 and -1.301708279.

Subproblem 1
m + 0.8333333335 = 1.301708279

Simplifying
m + 0.8333333335 = 1.301708279

Reorder the terms:
0.8333333335 + m = 1.301708279

Solving
0.8333333335 + m = 1.301708279

Solving for variable 'm'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + m = 1.301708279 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + m = 1.301708279 + -0.8333333335
m = 1.301708279 + -0.8333333335

Combine like terms: 1.301708279 + -0.8333333335 = 0.4683749455
m = 0.4683749455

Simplifying
m = 0.4683749455

Subproblem 2
m + 0.8333333335 = -1.301708279

Simplifying
m + 0.8333333335 = -1.301708279

Reorder the terms:
0.8333333335 + m = -1.301708279

Solving
0.8333333335 + m = -1.301708279

Solving for variable 'm'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + m = -1.301708279 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + m = -1.301708279 + -0.8333333335
m = -1.301708279 + -0.8333333335

Combine like terms: -1.301708279 + -0.8333333335 = -2.1350416125
m = -2.1350416125

Simplifying
m = -2.1350416125

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.4683749455, -2.1350416125}
Solution
m = {0.4683749455, -2.1350416125}