x^2-4nx+3n^2=0

Solution for x^2-4nx+3n^2=0 equation:

Simplifying
x2 + -4nx + 3n2 = 0

Reorder the terms:
-4nx + 3n2 + x2 = 0

Solving
-4nx + 3n2 + x2 = 0

Solving for variable 'n'.

Factor a trinomial.
(n + -1x)(3n + -1x) = 0

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

Simplifying
n + -1x = 0

Solving
n + -1x = 0

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

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

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

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

Simplifying
3n + -1x = 0

Solving
3n + -1x = 0

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

Add 'x' to each side of the equation.
3n + -1x + x = 0 + x

Combine like terms: -1x + x = 0
3n + 0 = 0 + x
3n = 0 + x
Remove the zero:
3n = x

Divide each side by '3'.
n = 0.3333333333x

Simplifying
n = 0.3333333333x
Solution
n = {x, 0.3333333333x}