My 2013 535i had this annoying shake at stoplights for months and I just lived with it. Finally got tired of it and took the car to a specialist. They confirmed both engine mounts were collapsed and leaking fluid. Got the Dubai Engine Mount Replacement BMW done at a shop that works on German cars. The mechanic showed me the old mounts – they were almost flat compared to the new ones. After the replacement, the car feels like it just rolled off the showroom floor. No more vibrations, no more weird clunk when shifting into drive. Cost was reasonable and the job took about three hours. If your BMW shakes at idle, don't ignore it like I did. New mounts made the car feel brand new again. Very happy I finally did it.