3m^2-my-2y^2=0

Solution for 3m^2-my-2y^2=0 equation:

Simplifying
3m2 + -1my + -2y2 = 0

Reorder the terms:
-1my + 3m2 + -2y2 = 0

Solving
-1my + 3m2 + -2y2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -1y)(3m + 2y) = 0

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

Simplifying
m + -1y = 0

Solving
m + -1y = 0

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

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

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

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

Simplifying
3m + 2y = 0

Solving
3m + 2y = 0

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

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

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

Divide each side by '3'.
m = -0.6666666667y

Simplifying
m = -0.6666666667y
Solution
m = {y, -0.6666666667y}