My 2007 450 sportsman won.t start but she backfires

Various ideas in the link.

Engines only need three things

Good fresh fuel to the engine.
A spark at the right time
Compression

https://www.google.com/search?q=2004+Polaris+Sportsman+700.+Crank+but+no+start

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Go back to basics. What EXACTLY does it do when you try to start it? Just spins it is often No spark. 'Coughs' and tries to start is possibly a fuel supply issue.
An engine needs 3 things to run. Air, Fuel, Spark. Did you check for spark on both cylinders?
Have you checked the air filter is clean. You will be surprised at how much a dirty one can affect an engine.
Have you checked for fuel supply at the cylinders. If you can get your head near the plug holes try this. Remove both spark plugs. Crank the engine for 2 seconds then remove the ignition key. Sniff the spark plug hole. Does it smell of fuel? Do the same for the other cylinder. Use the comment button below and I'll see if I can help you more.

check cap vent -fuel filter - valve - carb problem

do you have spark? if not I'd start checking the safety interlocks, kill switches, key, etc

Remove and clean the plug, sounds like it is fouled.

replace fuel filter. check spark plug. fuel has waste in it bad fuel maybe.. has it been setting a long time. remove sediment bowl from carb. should at least drain the carb and catch the fuel from the drain. examine fuel caught for bubbles in bottom of fuel container. air filter clean? adj timing ? does it smoke when running? backfire? choke off ?

sounds like an air leak and or adjust valves

3 things you need to check
1. spark (blue or white good) (orang or yellow bad)
2. fuel
3. compression

check in ignition system.something heating up.

carbon on the plugs indicates flooding
the backfire indicates fuel being ignited in the exhaust
have the carby /fuel system professionally overhauled