4*s^3+12*s^2+10*s=0

Solution for 4*s^3+12*s^2+10*s=0 equation:

Simplifying
4s3 + 12s2 + 10s = 0

Reorder the terms:
10s + 12s2 + 4s3 = 0

Solving
10s + 12s2 + 4s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2s'.
2s(5 + 6s + 2s2) = 0

Ignore the factor 2.
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 + 6s + 2s2)' equal to zero and attempt to solve:

Simplifying
5 + 6s + 2s2 = 0

Solving
5 + 6s + 2s2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
2.5 + 3s + s2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 3s + -2.5 + s2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 3s + s2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 3s + s2 = 0 + -2.5
3s + s2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
3s + s2 = -2.5

The s term is 3s.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3s + 2.25 + s2 = -2.5 + 2.25

Reorder the terms:
2.25 + 3s + s2 = -2.5 + 2.25

Combine like terms: -2.5 + 2.25 = -0.25
2.25 + 3s + s2 = -0.25

Factor a perfect square on the left side:
(s + 1.5)(s + 1.5) = -0.25

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}