Small Engines (Lawn Mowers, etc.): Craftsman 16.5 HP B&S lawn tractor model # 917.271634 s/n 080701D016693 backfires and wont start, side discharge, tractor model

Question
My lawn tractor has been running ruff the last two or three times I have moved the grass.  I checked the plug for fire and it was OK, I also cleaned it. I put in a new filter, changed the gas and put in a new fuel filter.  It ran ruff for about 5-10 minutes each time while mowing then it would smooth out.  When I would turn the ignition off, it would backfire some.  Today the battery would not turn over the engine, so I charge it for about 30 minutes.  I then fired it up, it was running ruff and black smoke was coming out the muffler. I engaged the blades and mower for about 90 feet and then it started running smooth. I stopped and turned the mover off to remove the side discharge/mulching cover.  I got back on the mover and turned the ignition.  It backfired one loud time and black smoke came from the muffler and would not fire again.  What do I do now?

Answer
take a look at your fuel shutoff solenoid located on the bottom of the carburetor.  Touch it, does it feel like the pin is open and closing when u turn the power on and off to it?  

If this is working properly lets check the carb bowl for dirt.  Clean the carb,

And if this is still a problem we may need to look at the valves and or timing key.    There is a VERY slim chance you have a bad camshaft.