2S^2+4S+2=0

Solution for 2S^2+4S+2=0 equation:

Simplifying
2S2 + 4S + 2 = 0

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

Solving
2 + 4S + 2S2 = 0

Solving for variable 'S'.

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

Factor a trinomial.
2((1 + S)(1 + S)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + S)' equal to zero and attempt to solve:

Simplifying
1 + S = 0

Solving
1 + S = 0

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

Add '-1' to each side of the equation.
1 + -1 + S = 0 + -1

Combine like terms: 1 + -1 = 0
0 + S = 0 + -1
S = 0 + -1

Combine like terms: 0 + -1 = -1
S = -1

Simplifying
S = -1
Subproblem 2
Set the factor '(1 + S)' equal to zero and attempt to solve:

Simplifying
1 + S = 0

Solving
1 + S = 0

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

Add '-1' to each side of the equation.
1 + -1 + S = 0 + -1

Combine like terms: 1 + -1 = 0
0 + S = 0 + -1
S = 0 + -1

Combine like terms: 0 + -1 = -1
S = -1

Simplifying
S = -1
Solution
S = {-1, -1}