4m+2mn=m^2+m+3m^2

Solution for 4m+2mn=m^2+m+3m^2 equation:

Simplifying
4m + 2mn = m2 + m + 3m2

Reorder the terms:
4m + 2mn = m + m2 + 3m2

Combine like terms: m2 + 3m2 = 4m2
4m + 2mn = m + 4m2

Solving
4m + 2mn = m + 4m2

Solving for variable 'm'.

Reorder the terms:
4m + -1m + 2mn + -4m2 = m + 4m2 + -1m + -4m2

Combine like terms: 4m + -1m = 3m
3m + 2mn + -4m2 = m + 4m2 + -1m + -4m2

Reorder the terms:
3m + 2mn + -4m2 = m + -1m + 4m2 + -4m2

Combine like terms: m + -1m = 0
3m + 2mn + -4m2 = 0 + 4m2 + -4m2
3m + 2mn + -4m2 = 4m2 + -4m2

Combine like terms: 4m2 + -4m2 = 0
3m + 2mn + -4m2 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(3 + 2n + -4m) = 0

Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(3 + 2n + -4m)' equal to zero and attempt to solve:

Simplifying
3 + 2n + -4m = 0

Reorder the terms:
3 + -4m + 2n = 0

Solving
3 + -4m + 2n = 0

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

Add '-3' to each side of the equation.
3 + -4m + -3 + 2n = 0 + -3

Reorder the terms:
3 + -3 + -4m + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4m + 2n = 0 + -3
-4m + 2n = 0 + -3

Combine like terms: 0 + -3 = -3
-4m + 2n = -3

Add '-2n' to each side of the equation.
-4m + 2n + -2n = -3 + -2n

Combine like terms: 2n + -2n = 0
-4m + 0 = -3 + -2n
-4m = -3 + -2n

Divide each side by '-4'.
m = 0.75 + 0.5n

Simplifying
m = 0.75 + 0.5n
Solution
m = {0, 0.75 + 0.5n}