w^2+5kw+4k^2=0

Solution for w^2+5kw+4k^2=0 equation:

Simplifying
w2 + 5kw + 4k2 = 0

Reorder the terms:
5kw + 4k2 + w2 = 0

Solving
5kw + 4k2 + w2 = 0

Solving for variable 'k'.

Factor a trinomial.
(4k + w)(k + w) = 0

Subproblem 1
Set the factor '(4k + w)' equal to zero and attempt to solve:

Simplifying
4k + w = 0

Solving
4k + w = 0

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

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

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

Divide each side by '4'.
k = -0.25w

Simplifying
k = -0.25w
Subproblem 2
Set the factor '(k + w)' equal to zero and attempt to solve:

Simplifying
k + w = 0

Solving
k + w = 0

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

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

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

Simplifying
k = -1w
Solution
k = {-0.25w, -1w}