m^2+mn-6n^2=0

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

Simplifying
m2 + mn + -6n2 = 0

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

Solving
mn + m2 + -6n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -2n)(m + 3n) = 0

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

Simplifying
m + -2n = 0

Solving
m + -2n = 0

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

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

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

Simplifying
m = 2n
Subproblem 2
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
Solution
m = {2n, -3n}