I'm trying to find all values of x that are NOT in the domain of g:

g(x) = x + 6 / x^2 + 12x + 36

What you posted means this:

I think you mean this: g(x) = (x + 6)/(x^2 + 12x + 36) which is

You can learn about typing out math

here.

I don't know how to factor the denominator. What are the rules on factoring something like this. I've scoured Purplemath for the answers but haven't had any luck. Thanks.

You searched for "factoring quadratics" and didn't come up with anything? Maybe the search was broken when you tried. Right now, I get this:

list
To start find factors of 36 that add up to 12.