=S^3+2S^2+4S

Solution for =S^3+2S^2+4S equation:

Simplifying
0 = S3 + 2S2 + 4S

Reorder the terms:
0 = 4S + 2S2 + S3

Solving
0 = 4S + 2S2 + S3

Solving for variable 'S'.
Remove the zero:
-4S + -2S2 + -1S3 = 4S + 2S2 + S3 + -4S + -2S2 + -1S3

Reorder the terms:
-4S + -2S2 + -1S3 = 4S + -4S + 2S2 + -2S2 + S3 + -1S3

Combine like terms: 4S + -4S = 0
-4S + -2S2 + -1S3 = 0 + 2S2 + -2S2 + S3 + -1S3
-4S + -2S2 + -1S3 = 2S2 + -2S2 + S3 + -1S3

Combine like terms: 2S2 + -2S2 = 0
-4S + -2S2 + -1S3 = 0 + S3 + -1S3
-4S + -2S2 + -1S3 = S3 + -1S3

Combine like terms: S3 + -1S3 = 0
-4S + -2S2 + -1S3 = 0

Factor out the Greatest Common Factor (GCF), '-1S'.
-1S(4 + 2S + S2) = 0

Ignore the factor -1.
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 '(4 + 2S + S2)' equal to zero and attempt to solve:

Simplifying
4 + 2S + S2 = 0

Solving
4 + 2S + S2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 2S + -4 + S2 = 0 + -4

Reorder the terms:
4 + -4 + 2S + S2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2S + S2 = 0 + -4
2S + S2 = 0 + -4

Combine like terms: 0 + -4 = -4
2S + S2 = -4

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 = -4 + 1

Reorder the terms:
1 + 2S + S2 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + 2S + S2 = -3

Factor a perfect square on the left side:
(S + 1)(S + 1) = -3

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}