2m^2+6mn+4n^2=

Solution for 2m^2+6mn+4n^2= equation:

Simplifying
2m2 + 6mn + 4n2 = 0

Reorder the terms:
6mn + 2m2 + 4n2 = 0

Solving
6mn + 2m2 + 4n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3mn + m2 + 2n2) = 0

Factor a trinomial.
2((m + n)(m + 2n)) = 0

Ignore the factor 2.
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 + 2n)' equal to zero and attempt to solve:

Simplifying
m + 2n = 0

Solving
m + 2n = 0

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

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

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

Simplifying
m = -2n
Solution
m = {-1n, -2n}