x^2-5kx+4k^2=0

Solution for x^2-5kx+4k^2=0 equation:

Simplifying
x2 + -5kx + 4k2 = 0

Reorder the terms:
-5kx + 4k2 + x2 = 0

Solving
-5kx + 4k2 + x2 = 0

Solving for variable 'k'.

Factor a trinomial.
(k + -1x)(4k + -1x) = 0

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

Simplifying
k + -1x = 0

Solving
k + -1x = 0

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

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

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

Simplifying
k = x
Subproblem 2
Set the factor '(4k + -1x)' equal to zero and attempt to solve:

Simplifying
4k + -1x = 0

Solving
4k + -1x = 0

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

Add 'x' to each side of the equation.
4k + -1x + x = 0 + x

Combine like terms: -1x + x = 0
4k + 0 = 0 + x
4k = 0 + x
Remove the zero:
4k = x

Divide each side by '4'.
k = 0.25x

Simplifying
k = 0.25x
Solution
k = {x, 0.25x}