(f+2)(f+6)=0

Solution for (f+2)(f+6)=0 equation:

Simplifying
(f + 2)(f + 6) = 0

Reorder the terms:
(2 + f)(f + 6) = 0

Reorder the terms:
(2 + f)(6 + f) = 0

Multiply (2 + f) * (6 + f)
(2(6 + f) + f(6 + f)) = 0
((6 * 2 + f * 2) + f(6 + f)) = 0
((12 + 2f) + f(6 + f)) = 0
(12 + 2f + (6 * f + f * f)) = 0
(12 + 2f + (6f + f2)) = 0

Combine like terms: 2f + 6f = 8f
(12 + 8f + f2) = 0

Solving
12 + 8f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(6 + f)(2 + f) = 0

Subproblem 1
Set the factor '(6 + f)' equal to zero and attempt to solve:

Simplifying
6 + f = 0

Solving
6 + f = 0

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

Add '-6' to each side of the equation.
6 + -6 + f = 0 + -6

Combine like terms: 6 + -6 = 0
0 + f = 0 + -6
f = 0 + -6

Combine like terms: 0 + -6 = -6
f = -6

Simplifying
f = -6
Subproblem 2
Set the factor '(2 + f)' equal to zero and attempt to solve:

Simplifying
2 + f = 0

Solving
2 + f = 0

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

Add '-2' to each side of the equation.
2 + -2 + f = 0 + -2

Combine like terms: 2 + -2 = 0
0 + f = 0 + -2
f = 0 + -2

Combine like terms: 0 + -2 = -2
f = -2

Simplifying
f = -2
Solution
f = {-6, -2}