4f^2+12f+5=0

Solution for 4f^2+12f+5=0 equation:

Simplifying
4f2 + 12f + 5 = 0

Reorder the terms:
5 + 12f + 4f2 = 0

Solving
5 + 12f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(5 + 2f)(1 + 2f) = 0

Subproblem 1
Set the factor '(5 + 2f)' equal to zero and attempt to solve:

Simplifying
5 + 2f = 0

Solving
5 + 2f = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2f = 0 + -5
2f = 0 + -5

Combine like terms: 0 + -5 = -5
2f = -5

Divide each side by '2'.
f = -2.5

Simplifying
f = -2.5
Subproblem 2
Set the factor '(1 + 2f)' equal to zero and attempt to solve:

Simplifying
1 + 2f = 0

Solving
1 + 2f = 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 + 2f = 0 + -1

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

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

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

Simplifying
f = -0.5
Solution
f = {-2.5, -0.5}