5f^2+21f+4=0

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

Simplifying
5f2 + 21f + 4 = 0

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

Solving
4 + 21f + 5f2 = 0

Solving for variable 'f'.

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

Subproblem 1
Set the factor '(4 + f)' equal to zero and attempt to solve:

Simplifying
4 + f = 0

Solving
4 + f = 0

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

Add '-4' to each side of the equation.
4 + -4 + f = 0 + -4

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

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

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

Simplifying
1 + 5f = 0

Solving
1 + 5f = 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 + 5f = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5f = 0 + -1
5f = 0 + -1

Combine like terms: 0 + -1 = -1
5f = -1

Divide each side by '5'.
f = -0.2

Simplifying
f = -0.2
Solution
f = {-4, -0.2}