86 Honda shadow will fire but won't stay running when it does it idols rough and backfires a lot removed the carbs and cleaned them but still have the problem any ideas about how to get it to run?

your plugs may be fouled. pull them and check for carbon buid-up, discoloration, etc. you may be able to clean them and adjust the gap. also, very much sounds like a timing problem. the timing could be off just enough to permit the bike to start but will not accept throttle, idles rough, & small back-fires through the carbs. hope this helps