m^2-7(mn)+12n^2=0

Solution for m^2-7(mn)+12n^2=0 equation:

Simplifying
m2 + -7(mn) + 12n2 = 0

Reorder the terms:
-7mn + m2 + 12n2 = 0

Solving
-7mn + m2 + 12n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -4n)(m + -3n) = 0

Subproblem 1
Set the factor '(m + -4n)' equal to zero and attempt to solve:

Simplifying
m + -4n = 0

Solving
m + -4n = 0

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

Add '4n' to each side of the equation.
m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
m + 0 = 0 + 4n
m = 0 + 4n
Remove the zero:
m = 4n

Simplifying
m = 4n
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 = {4n, 3n}