f^2+12f+32=0

Solution for f^2+12f+32=0 equation:

Simplifying
f2 + 12f + 32 = 0

Reorder the terms:
32 + 12f + f2 = 0

Solving
32 + 12f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(8 + f)(4 + 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 '(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
Solution
f = {-8, -4}