Both of the rear turn signals stopped working at the same time, but everything else seems to work. Do you know what can cause this to happen? I changed one of the bulbs and it didn't work.

There is a turn signal flasher under dash...most have a flasher for the emergency signals and one for the turn signals...some have one flasher....but check fuses first...normally it is fuse burnt...if you can locate the flasher normally they will get abnormally warm when bad......it should look like a round or square silver shiney or black cube.........if these are good with ign.on hold turn signal lever down firmly ...if it works replace turn signal unit.....if none of this works you have to troubleshoot wiring...
...normally yellow wire is left turn and green wire is right turn...black or white is ground red is stop light....but normally it is a blown fuse or flasher.

Check fuses. switch new bulb to otherside .check to see if there is power to socket if not could be broken wire.