2m^2-5mn-3n^2=0

Solution for 2m^2-5mn-3n^2=0 equation:

Simplifying
2m2 + -5mn + -3n2 = 0

Reorder the terms:
-5mn + 2m2 + -3n2 = 0

Solving
-5mn + 2m2 + -3n2 = 0

Solving for variable 'm'.

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

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

Simplifying
m + -3n = 0

Solving
m + -3n = 0

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

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

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

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

Simplifying
2m + n = 0

Solving
2m + n = 0

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

Add '-1n' to each side of the equation.
2m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
2m + 0 = 0 + -1n
2m = 0 + -1n
Remove the zero:
2m = -1n

Divide each side by '2'.
m = -0.5n

Simplifying
m = -0.5n
Solution
m = {3n, -0.5n}