18m^2-5mn-2n^2=0

Solution for 18m^2-5mn-2n^2=0 equation:

Simplifying
18m2 + -5mn + -2n2 = 0

Reorder the terms:
-5mn + 18m2 + -2n2 = 0

Solving
-5mn + 18m2 + -2n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + -1n)(9m + 2n) = 0

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

Simplifying
2m + -1n = 0

Solving
2m + -1n = 0

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

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

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

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

Simplifying
m = 0.5n
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 = {0.5n, -0.2222222222n}