f^2+8f+15=0

Solution for f^2+8f+15=0 equation:

Simplifying
f2 + 8f + 15 = 0

Reorder the terms:
15 + 8f + f2 = 0

Solving
15 + 8f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(5 + f)(3 + f) = 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 '(3 + f)' equal to zero and attempt to solve:

Simplifying
3 + f = 0

Solving
3 + f = 0

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

Add '-3' to each side of the equation.
3 + -3 + f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + f = 0 + -3
f = 0 + -3

Combine like terms: 0 + -3 = -3
f = -3

Simplifying
f = -3
Solution
f = {-5, -3}