x^2+4kx=5k^2

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

Simplifying
x2 + 4kx = 5k2

Reorder the terms:
4kx + x2 = 5k2

Solving
4kx + x2 = 5k2

Solving for variable 'k'.

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

Combine like terms: 5k2 + -5k2 = 0
4kx + -5k2 + x2 = 0

Factor a trinomial.
(-5k + -1x)(k + -1x) = 0

Subproblem 1
Set the factor '(-5k + -1x)' equal to zero and attempt to solve:

Simplifying
-5k + -1x = 0

Solving
-5k + -1x = 0

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

Add 'x' to each side of the equation.
-5k + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-5k + 0 = 0 + x
-5k = 0 + x
Remove the zero:
-5k = x

Divide each side by '-5'.
k = -0.2x

Simplifying
k = -0.2x
Subproblem 2
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
Solution
k = {-0.2x, x}