s^3-2s^2+5s=0

Solution for s^3-2s^2+5s=0 equation:

Simplifying
s3 + -2s2 + 5s = 0

Reorder the terms:
5s + -2s2 + s3 = 0

Solving
5s + -2s2 + s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), 's'.
s(5 + -2s + s2) = 0

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

Simplifying
s = 0

Solving
s = 0

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

Simplifying
s = 0
Subproblem 2
Set the factor '(5 + -2s + s2)' equal to zero and attempt to solve:

Simplifying
5 + -2s + s2 = 0

Solving
5 + -2s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -2s + -5 + s2 = 0 + -5

Reorder the terms:
5 + -5 + -2s + s2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2s + s2 = 0 + -5
-2s + s2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2s + s2 = -5

The s term is -2s.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2s + 1 + s2 = -5 + 1

Reorder the terms:
1 + -2s + s2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + -2s + s2 = -4

Factor a perfect square on the left side:
(s + -1)(s + -1) = -4

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
s = {0}