m^2+4mn-5n^2=

Solution for m^2+4mn-5n^2= equation:

Simplifying
m2 + 4mn + -5n2 = 0

Reorder the terms:
4mn + m2 + -5n2 = 0

Solving
4mn + m2 + -5n2 = 0

Solving for variable 'm'.

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

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

Simplifying
m + -1n = 0

Solving
m + -1n = 0

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

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

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

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

Simplifying
m + 5n = 0

Solving
m + 5n = 0

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

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

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

Simplifying
m = -5n
Solution
m = {n, -5n}