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

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

Simplifying
4m2 + 2mn + -12n2 = 0

Reorder the terms:
2mn + 4m2 + -12n2 = 0

Solving
2mn + 4m2 + -12n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(mn + 2m2 + -6n2) = 0

Factor a trinomial.
2((2m + -3n)(m + 2n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2m + -3n)' equal to zero and attempt to solve:

Simplifying
2m + -3n = 0

Solving
2m + -3n = 0

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

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

Combine like terms: -3n + 3n = 0
2m + 0 = 0 + 3n
2m = 0 + 3n
Remove the zero:
2m = 3n

Divide each side by '2'.
m = 1.5n

Simplifying
m = 1.5n
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 = {1.5n, -2n}