Is it even possible to set up a system in 12x12 room?

It all depends. If its any consolation, I have 2 very different 12X12 rooms set up pretty well these days. One in particular is especially challenging, the other not so much. So yes it can be done. Way more things will work well in a small room compared to a large one. The key to any room offering tight quarters is often that less = more. With that in mind, just try different things and see what works out best.

Whenever quarters are tight and the listening position cannot be far from speakers, I tend to steer away from larger speakers with widely spaced drivers, like many but not all tower designs. Those usually require farther distance to listening position for the drivers to mesh properly.

In my tougher room, my wife’s acoustically challenged sun room with hard tile floor,  lots of windows and cathedral ceiling, I’ve settled currently on a pair of Vanatoo Transparent One Encore speakers (on very short isolating floor stands located near corners and angled up slightly) that work fabulously well in there. They also happen to be the smallest and least expensive speakers I’ve ever tried in there.

My other room is more conventional size and construction (couch near rear wall also) and my main gear is located there. Currently I run a pair of Kef ls50s with a separate powered sub there, but I’ve run many other suitable monitors and floor standers there as well also with very good results over the years.

Another consideration is speakers that are designed for placement very close to the wall or even the corners that will give you more room in the room for your listening space. 

I moved from a 26x18 room to a 11x14 room and found the larger system would just not work in the smaller room so I went to smaller stand mount monitors ( Sonus Fabers) that worked well with some room treatment. after a year I got a set of AudioNote ANE's and they sat in the corners and gave me the bass back I was missing from the monitors and with the room treatment sounded great. I had an open double door behind my chair so I was able to get back further from the speakers. 

https://systems.audiogon.com/systems/7605

My office is the same size as your room and it sounds pretty amazing now. I am going to put a new system in there since I figured out how to tame the room. I am looking at a few small floor standers and also very large bookshelf speakers as the next speaker for this room.

I started a thread last December that helped me figure out how to tame this room. I was considering using DSP along with acoustic treatments, however, now I think acoustic treatments is all I need. Tone controls maybe useful in the next preamp I get.

https://forum.audiogon.com/discussions/big-speakers-in-small-room-at-moderate-volume-levels

I’ve got a system set up against a 12ft short wall and on the living room end of a long (almost hallway-like) dining/living room space (old 2/1 bungalow, baby). Locked into that position as the entire length is mid-flanked by the fireplace and entry way/front door. At first I thought t would be too much, but with even minor room adjustments, it’s really pretty nice. Definitely seems, however, small treatments make an almost exponential difference, that part has been tricky. Had to work with the wifey on “compromises” ie blanket ladder, hell yes!...huge mirror, hell no!!...etc.

Sure, I'm getting excellent sound in my temporary apartment in a room roughly that size. Obviously speaker dependent.  fear not!