w^4+17w^3+75w^2=0

Solution for w^4+17w^3+75w^2=0 equation:

Simplifying
w4 + 17w3 + 75w2 = 0

Reorder the terms:
75w2 + 17w3 + w4 = 0

Solving
75w2 + 17w3 + w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w2'.
w2(75 + 17w + w2) = 0

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 '(75 + 17w + w2)' equal to zero and attempt to solve:

Simplifying
75 + 17w + w2 = 0

Solving
75 + 17w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + 17w + -75 + w2 = 0 + -75

Reorder the terms:
75 + -75 + 17w + w2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + 17w + w2 = 0 + -75
17w + w2 = 0 + -75

Combine like terms: 0 + -75 = -75
17w + w2 = -75

The w term is 17w.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17w + 72.25 + w2 = -75 + 72.25

Reorder the terms:
72.25 + 17w + w2 = -75 + 72.25

Combine like terms: -75 + 72.25 = -2.75
72.25 + 17w + w2 = -2.75

Factor a perfect square on the left side:
(w + 8.5)(w + 8.5) = -2.75

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}