m^2-4km+3k^2=0

Solution for m^2-4km+3k^2=0 equation:

Simplifying
m2 + -4km + 3k2 = 0

Reorder the terms:
-4km + 3k2 + m2 = 0

Solving
-4km + 3k2 + m2 = 0

Solving for variable 'k'.

Factor a trinomial.
(k + -1m)(3k + -1m) = 0

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

Simplifying
k + -1m = 0

Solving
k + -1m = 0

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

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

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

Simplifying
k = m
Subproblem 2
Set the factor '(3k + -1m)' equal to zero and attempt to solve:

Simplifying
3k + -1m = 0

Solving
3k + -1m = 0

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

Add 'm' to each side of the equation.
3k + -1m + m = 0 + m

Combine like terms: -1m + m = 0
3k + 0 = 0 + m
3k = 0 + m
Remove the zero:
3k = m

Divide each side by '3'.
k = 0.3333333333m

Simplifying
k = 0.3333333333m
Solution
k = {m, 0.3333333333m}