9m^2-25mn-6n^2=0

Solution for 9m^2-25mn-6n^2=0 equation:

Simplifying
9m2 + -25mn + -6n2 = 0

Reorder the terms:
-25mn + 9m2 + -6n2 = 0

Solving
-25mn + 9m2 + -6n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -3n)(9m + 2n) = 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 '(9m + 2n)' equal to zero and attempt to solve:

Simplifying
9m + 2n = 0

Solving
9m + 2n = 0

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

Add '-2n' to each side of the equation.
9m + 2n + -2n = 0 + -2n

Combine like terms: 2n + -2n = 0
9m + 0 = 0 + -2n
9m = 0 + -2n
Remove the zero:
9m = -2n

Divide each side by '9'.
m = -0.2222222222n

Simplifying
m = -0.2222222222n
Solution
m = {3n, -0.2222222222n}