m^2-4mn-12n^2=0

Solution for m^2-4mn-12n^2=0 equation:

Simplifying
m2 + -4mn + -12n2 = 0

Reorder the terms:
-4mn + m2 + -12n2 = 0

Solving
-4mn + m2 + -12n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -6n)(m + 2n) = 0

Subproblem 1
Set the factor '(m + -6n)' equal to zero and attempt to solve:

Simplifying
m + -6n = 0

Solving
m + -6n = 0

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

Add '6n' to each side of the equation.
m + -6n + 6n = 0 + 6n

Combine like terms: -6n + 6n = 0
m + 0 = 0 + 6n
m = 0 + 6n
Remove the zero:
m = 6n

Simplifying
m = 6n
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 = {6n, -2n}