m^2=5mn+6n^2

Solution for m^2=5mn+6n^2 equation:

Simplifying
m2 = 5mn + 6n2

Solving
m2 = 5mn + 6n2

Solving for variable 'm'.

Reorder the terms:
-5mn + m2 + -6n2 = 5mn + 6n2 + -5mn + -6n2

Reorder the terms:
-5mn + m2 + -6n2 = 5mn + -5mn + 6n2 + -6n2

Combine like terms: 5mn + -5mn = 0
-5mn + m2 + -6n2 = 0 + 6n2 + -6n2
-5mn + m2 + -6n2 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
-5mn + m2 + -6n2 = 0

Factor a trinomial.
(m + -6n)(m + n) = 0

Subproblem 1
Set the factor '(m + -6n)' equal to zero and attempt to solve:

Simplifying
m + -6n = 0

Solving
m + -6n = 0

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

Add '6n' to each side of the equation.
m + -6n + 6n = 0 + 6n

Combine like terms: -6n + 6n = 0
m + 0 = 0 + 6n
m = 0 + 6n
Remove the zero:
m = 6n

Simplifying
m = 6n
Subproblem 2
Set the factor '(m + n)' equal to zero and attempt to solve:

Simplifying
m + n = 0

Solving
m + n = 0

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

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

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

Simplifying
m = -1n
Solution
m = {6n, -1n}