5f^2+41f+8=0

Solution for 5f^2+41f+8=0 equation:

Simplifying
5f2 + 41f + 8 = 0

Reorder the terms:
8 + 41f + 5f2 = 0

Solving
8 + 41f + 5f2 = 0

Solving for variable 'f'.

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

Subproblem 1
Set the factor '(8 + f)' equal to zero and attempt to solve:

Simplifying
8 + f = 0

Solving
8 + f = 0

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

Add '-8' to each side of the equation.
8 + -8 + f = 0 + -8

Combine like terms: 8 + -8 = 0
0 + f = 0 + -8
f = 0 + -8

Combine like terms: 0 + -8 = -8
f = -8

Simplifying
f = -8
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 = {-8, -0.2}