f^2+13f+40=0

Solution for f^2+13f+40=0 equation:

Simplifying
f2 + 13f + 40 = 0

Reorder the terms:
40 + 13f + f2 = 0

Solving
40 + 13f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(8 + f)(5 + f) = 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 '(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
Solution
f = {-8, -5}