Forums are like computers
Junk in results in junk out
If you want meaningful responses then we need to model trim & serial numbers
And the make model & serial of whatever the B & S is attached to won't hurt either
Otherwise all you will get is generic information.
<rant>This is SO much BS. The make, model, and serial number have NOTHING to do with mixture, spark, and compression. You're trying to punish the poster with demands for irrelevant information. SPEAK TO THE ISSUE! Regardless of make, model, and serial number, the poster's problem is not that he has the any specific make or model, but that his engine won't start for 30 minutes after he shuts it off. He's not alone in having this issue, and I'd bet money that others who have this issue have DIFFERENT makes and models. Forum Nazis who think that everyone should provide infinite boring detail to ask a simple question are just the worst.</rant>
Now to the issue at hand:
WHY won't the poster's mower start? Offhand, I can think of several possible causes:
1. If the mower stopped because it was out of gas: Maybe there was some floating dust or debris on top of the gas that got sucked into the carburetor. If this is the case, you'll probably need to get a spray can of "starting fluid." Take the air filter off. There's a small hole under the filter where air gets sucked through the filter into the engine. Douche that hole with starting fluid, and then have someone pull the starter cord. The engine should run for a few seconds and then slow to a stop. If so, repeat this process, but while the engine's trying to run, put your thumb over the air inlet hole. This creates a tremendous vacuum at the fuel jet, and will often dislodge trash. You may have to do it a few times...
2. If the mower wouldn't start at all, you may have some water in your gas. This could come from your gas can or even from atmospheric condensation. Water droplets do NOT want to pass through the fuel jet. You may be able to get through this by pouring some "Sea Foam" additive into the gas tank and then using Step 1 above to clear the fuel jet.
3. Before doing any of this, inspect the air filter. Is it so dirty that it's plugged? You can spend time cleaning it, but I just buy a new one at the start of each mowing season (and keep a spare on hand, just in case). The darned foam filters can appear semi-clean but still have gunk inside them. To check the filter, just take it off & try to start the engine. Starts normally? Get a new filter.
4. Check the spark-plug wire. Is it firmly attached to the plug, or did some branch reach up and pull it off? Not attached = no spark. In general, the plug itself lasts the life of the mower, so don't bother pulling it except as a last resort.
Of all the above, Numbers 1 & 2 have been the most effective for me in fixing the "doesn't want to start right" syndrome. Best of luck, amigo!