4f^2+21f+5=0

Solution for 4f^2+21f+5=0 equation:

Simplifying
4f2 + 21f + 5 = 0

Reorder the terms:
5 + 21f + 4f2 = 0

Solving
5 + 21f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(5 + f)(1 + 4f) = 0

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

Simplifying
5 + f = 0

Solving
5 + f = 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 + f = 0 + -5

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

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

Simplifying
f = -5
Subproblem 2
Set the factor '(1 + 4f)' equal to zero and attempt to solve:

Simplifying
1 + 4f = 0

Solving
1 + 4f = 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 + 4f = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4f = 0 + -1
4f = 0 + -1

Combine like terms: 0 + -1 = -1
4f = -1

Divide each side by '4'.
f = -0.25

Simplifying
f = -0.25
Solution
f = {-5, -0.25}