4k^3w+20k^2w^2+25kw^3=0

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Solution for 4k^3w+20k^2w^2+25kw^3=0 equation: 


Simplifying
4k3w + 20k2w2 + 25kw3 = 0

Reorder the terms:
25kw3 + 20k2w2 + 4k3w = 0

Solving
25kw3 + 20k2w2 + 4k3w = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'kw'.
kw(25w2 + 20kw + 4k2) = 0

Factor a trinomial.
kw((5w + 2k)(5w + 2k)) = 0


Subproblem 1
Set the factor 'kw' equal to zero and attempt to solve:

Simplifying
kw = 0

Solving
kw = 0

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

Simplifying
kw = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(5w + 2k)' equal to zero and attempt to solve:

Simplifying
5w + 2k = 0

Reorder the terms:
2k + 5w = 0

Solving
2k + 5w = 0

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

Add '-5w' to each side of the equation.
2k + 5w + -5w = 0 + -5w

Combine like terms: 5w + -5w = 0
2k + 0 = 0 + -5w
2k = 0 + -5w
Remove the zero:
2k = -5w

Divide each side by '2'.
k = -2.5w

Simplifying
k = -2.5w

Subproblem 3
Set the factor '(5w + 2k)' equal to zero and attempt to solve:

Simplifying
5w + 2k = 0

Reorder the terms:
2k + 5w = 0

Solving
2k + 5w = 0

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

Add '-5w' to each side of the equation.
2k + 5w + -5w = 0 + -5w

Combine like terms: 5w + -5w = 0
2k + 0 = 0 + -5w
2k = 0 + -5w
Remove the zero:
2k = -5w

Divide each side by '2'.
k = -2.5w

Simplifying
k = -2.5w
Solution
k = {-2.5w, -2.5w}

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