12m^2-5mn-2n^2=0

Solution for 12m^2-5mn-2n^2=0 equation:

Simplifying
12m2 + -5mn + -2n2 = 0

Reorder the terms:
-5mn + 12m2 + -2n2 = 0

Solving
-5mn + 12m2 + -2n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(3m + -2n)(4m + n) = 0

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

Simplifying
3m + -2n = 0

Solving
3m + -2n = 0

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

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

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

Divide each side by '3'.
m = 0.6666666667n

Simplifying
m = 0.6666666667n
Subproblem 2
Set the factor '(4m + n)' equal to zero and attempt to solve:

Simplifying
4m + n = 0

Solving
4m + n = 0

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

Add '-1n' to each side of the equation.
4m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
4m + 0 = 0 + -1n
4m = 0 + -1n
Remove the zero:
4m = -1n

Divide each side by '4'.
m = -0.25n

Simplifying
m = -0.25n
Solution
m = {0.6666666667n, -0.25n}