10s^3-22s^2+4s=2s

Solution for 10s^3-22s^2+4s=2s equation:

Simplifying
10s3 + -22s2 + 4s = 2s

Reorder the terms:
4s + -22s2 + 10s3 = 2s

Solving
4s + -22s2 + 10s3 = 2s

Solving for variable 's'.

Reorder the terms:
4s + -2s + -22s2 + 10s3 = 2s + -2s

Combine like terms: 4s + -2s = 2s
2s + -22s2 + 10s3 = 2s + -2s

Combine like terms: 2s + -2s = 0
2s + -22s2 + 10s3 = 0

Factor out the Greatest Common Factor (GCF), '2s'.
2s(1 + -11s + 5s2) = 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 '(1 + -11s + 5s2)' equal to zero and attempt to solve:

Simplifying
1 + -11s + 5s2 = 0

Solving
1 + -11s + 5s2 = 0

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

Divide each side by '5'.
0.2 + -2.2s + s2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -2.2s + -0.2 + s2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -2.2s + s2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -2.2s + s2 = 0 + -0.2
-2.2s + s2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-2.2s + s2 = -0.2

The s term is -2.2s.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2s + 1.21 + s2 = -0.2 + 1.21

Reorder the terms:
1.21 + -2.2s + s2 = -0.2 + 1.21

Combine like terms: -0.2 + 1.21 = 1.01
1.21 + -2.2s + s2 = 1.01

Factor a perfect square on the left side:
(s + -1.1)(s + -1.1) = 1.01

Calculate the square root of the right side: 1.004987562

Break this problem into two subproblems by setting 
(s + -1.1) equal to 1.004987562 and -1.004987562.

Subproblem 1
s + -1.1 = 1.004987562

Simplifying
s + -1.1 = 1.004987562

Reorder the terms:
-1.1 + s = 1.004987562

Solving
-1.1 + s = 1.004987562

Solving for variable 's'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + s = 1.004987562 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + s = 1.004987562 + 1.1
s = 1.004987562 + 1.1

Combine like terms: 1.004987562 + 1.1 = 2.104987562
s = 2.104987562

Simplifying
s = 2.104987562

Subproblem 2
s + -1.1 = -1.004987562

Simplifying
s + -1.1 = -1.004987562

Reorder the terms:
-1.1 + s = -1.004987562

Solving
-1.1 + s = -1.004987562

Solving for variable 's'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + s = -1.004987562 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + s = -1.004987562 + 1.1
s = -1.004987562 + 1.1

Combine like terms: -1.004987562 + 1.1 = 0.095012438
s = 0.095012438

Simplifying
s = 0.095012438

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {2.104987562, 0.095012438}
Solution
s = {0, 2.104987562, 0.095012438}