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

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

Simplifying
m2 + 4mn + 3n2 = 0

Reorder the terms:
4mn + m2 + 3n2 = 0

Solving
4mn + m2 + 3n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + n)(m + 3n) = 0

Subproblem 1
Set the factor '(m + n)' equal to zero and attempt to solve:

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

Simplifying
m + 3n = 0

Solving
m + 3n = 0

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

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

Combine like terms: 3n + -3n = 0
m + 0 = 0 + -3n
m = 0 + -3n
Remove the zero:
m = -3n

Simplifying
m = -3n
Solution
m = {-1n, -3n}