5w^4+25w^3+50w^2=0

Solution for 5w^4+25w^3+50w^2=0 equation:

Simplifying
5w4 + 25w3 + 50w2 = 0

Reorder the terms:
50w2 + 25w3 + 5w4 = 0

Solving
50w2 + 25w3 + 5w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w2'.
5w2(10 + 5w + w2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve:

Simplifying
w2 = 0

Solving
w2 = 0

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

Simplifying
w2 = 0

Take the square root of each side:
w = {0}
Subproblem 2
Set the factor '(10 + 5w + w2)' equal to zero and attempt to solve:

Simplifying
10 + 5w + w2 = 0

Solving
10 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 5w + -10 + w2 = 0 + -10

Reorder the terms:
10 + -10 + 5w + w2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 5w + w2 = 0 + -10
5w + w2 = 0 + -10

Combine like terms: 0 + -10 = -10
5w + w2 = -10

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = -10 + 6.25

Reorder the terms:
6.25 + 5w + w2 = -10 + 6.25

Combine like terms: -10 + 6.25 = -3.75
6.25 + 5w + w2 = -3.75

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
w = {0}