Mutiple cylinder misfire on 2000 Cadillac DeVille

I have a problem the car runs fine until it warms up then it runs with a mis when I hooked up the code meter it told me that both banks of cylinders were burning lean and I had random cylinder misfire can anyone help me solve this problem

Asked by for the 2000 Cadillac DeVille
What are the trouble codes that you retrieved?
The trouble codes that I recieved were P0300,P171,P174 Random Cylinder misfire and lean burn conditions on bank one and bank two cylinders ,I also removed the engine cover and I could hear some air sounding like a leak and also have a volt meter
Vehicle Application: 2002 Cadillac Deville 4.6L

Customer Concern: Rough idle, misfire. Powertrain Control Module (PCM) codes: P0171, P0174, P0300. OK at higher RPM. The throttle body boot was leaking.
Tests/Procedures: 1. Check for vacuum leak at the boot between the throttle body and the upper intake manifold plenum.

2. Spray water on the upper intake manifold, check for RPM response.
Potential Causes: Intake Manifold Gaskets
Throttle Body Boot

Tech Tips: A new throttle body boot fixed.
Diagnostic Codes: P0171, P0174, P0300
4 answers 2 comments
Look for a large air leak in the intake hoses and pipes. Beyond that, you need to get into diagnosing the fuel injection system, which involves special tools and experience. If you have a voltmeter you can do some checks, do you have one?
check to see if your belt tensioner is moving at all when the engine is running if so you need a new one. its easy to change. when its loose its sortof throwing off your timing causing a random misfire and hesitation.
Change all you Spark plugs.