8m^2-18mn-5n^2=0

Solution for 8m^2-18mn-5n^2=0 equation:

Simplifying
8m2 + -18mn + -5n2 = 0

Reorder the terms:
-18mn + 8m2 + -5n2 = 0

Solving
-18mn + 8m2 + -5n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + -5n)(4m + n) = 0

Subproblem 1
Set the factor '(2m + -5n)' equal to zero and attempt to solve:

Simplifying
2m + -5n = 0

Solving
2m + -5n = 0

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

Add '5n' to each side of the equation.
2m + -5n + 5n = 0 + 5n

Combine like terms: -5n + 5n = 0
2m + 0 = 0 + 5n
2m = 0 + 5n
Remove the zero:
2m = 5n

Divide each side by '2'.
m = 2.5n

Simplifying
m = 2.5n
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 = {2.5n, -0.25n}