3g^2+4g+1=0

Solution for 3g^2+4g+1=0 equation:

Simplifying
3g2 + 4g + 1 = 0

Reorder the terms:
1 + 4g + 3g2 = 0

Solving
1 + 4g + 3g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(1 + g)(1 + 3g) = 0

Subproblem 1
Set the factor '(1 + g)' equal to zero and attempt to solve:

Simplifying
1 + g = 0

Solving
1 + g = 0

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

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

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

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

Simplifying
g = -1
Subproblem 2
Set the factor '(1 + 3g)' equal to zero and attempt to solve:

Simplifying
1 + 3g = 0

Solving
1 + 3g = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3g = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3g = 0 + -1
3g = 0 + -1

Combine like terms: 0 + -1 = -1
3g = -1

Divide each side by '3'.
g = -0.3333333333

Simplifying
g = -0.3333333333
Solution
g = {-1, -0.3333333333}