4s^2+6s+2=0

Solution for 4s^2+6s+2=0 equation:

Simplifying
4s2 + 6s + 2 = 0

Reorder the terms:
2 + 6s + 4s2 = 0

Solving
2 + 6s + 4s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3s + 2s2) = 0

Factor a trinomial.
2((1 + s)(1 + 2s)) = 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 + 2s)' equal to zero and attempt to solve:

Simplifying
1 + 2s = 0

Solving
1 + 2s = 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 + 2s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2s = 0 + -1
2s = 0 + -1

Combine like terms: 0 + -1 = -1
2s = -1

Divide each side by '2'.
s = -0.5

Simplifying
s = -0.5
Solution
s = {-1, -0.5}