bf 750 trouble
For backfiring during deceleration, make sure your choke cable plungers on the carbs are closing ALL THE WAY when you turn off the choke (lever pushed all the way to the right). Slightly open choke plungers will let extra fuel into the carb. You have to "watch" each plunger as you (or your buddy) are pushing the lever. The plungers may get hung up due to the corrosion forming between the disimilar metals - brass plunger in the aluminum bore. Take them out and give a really good wipe with steel wool and spray some white lithim grease. Choke cable routing is important as well so that it doesn't bind or get pinched causing the plungers not to close all the way.
Most quad problems are caused by the loose NUT connecting the handle bar and the seat.