2n^2-9nm-35m^2=0

Solution for 2n^2-9nm-35m^2=0 equation:

Simplifying
2n2 + -9nm + -35m2 = 0

Reorder the terms:
-9mn + -35m2 + 2n2 = 0

Solving
-9mn + -35m2 + 2n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-5m + -2n)(7m + -1n) = 0

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

Simplifying
-5m + -2n = 0

Solving
-5m + -2n = 0

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

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

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

Divide each side by '-5'.
m = -0.4n

Simplifying
m = -0.4n
Subproblem 2
Set the factor '(7m + -1n)' equal to zero and attempt to solve:

Simplifying
7m + -1n = 0

Solving
7m + -1n = 0

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

Add 'n' to each side of the equation.
7m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
7m + 0 = 0 + n
7m = 0 + n
Remove the zero:
7m = n

Divide each side by '7'.
m = 0.1428571429n

Simplifying
m = 0.1428571429n
Solution
m = {-0.4n, 0.1428571429n}