Hint: f(x)=3^{x}+3^{-x} is an even function meaning that f(x)=f(-x)
Hi Espionage,
The easiest solution is to notice "by inspection" that 1 and -1 are roots. So the sum is 0. I'm not really that much of an arithmetic whiz. I drew the graph and then realized from the graph that 1 and -1 are the roots. Moral: always draw a picture if you can. Of course, use technology to draw said picture. Here's the graph that I drew together with the solutions as suggested above: