3f^2+4f+1=0

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

Simplifying
3f2 + 4f + 1 = 0

Reorder the terms:
1 + 4f + 3f2 = 0

Solving
1 + 4f + 3f2 = 0

Solving for variable 'f'.

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

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

Simplifying
1 + f = 0

Solving
1 + f = 0

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

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

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

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

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

Simplifying
1 + 3f = 0

Solving
1 + 3f = 0

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

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

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

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

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

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