Kawasaki gpz 1000 rx 1987 model

Running well at high revs would indicate that all the fuel and air it needs are getting to the engine and you also have a good spark. Probably no problem with air and fuel filter ( if fitted) or sparkplugs.

Running hot, and bad idling are signs of a lean air fuel mixture. The engine is probably not getting enough fuel at low revs.

This could be caused by an air leak between the carburettors and the engine. Check that the vacuum line to the fuel tap is properly secured at both ends. It is behind the fuel line at the tap.

Get a a short length of hollow plastic tube and use it like a stethascope - put one end to your ear and move the other end around your carburettor mounts with your engine revs as low as you can get, and listen for any sucking noises that would indicate a leak. Look for cracks in the rubber inlets.

The other possibility is that there is an internal blockage in the idling jets or idling fuel circuit. This is where dirt tends to lodge because the jet dimensions and passageways are very fine - The high speed jets are much bigger and dirt often just passes straight through.

Try a little bit of choke while the engine is warm to see if you get a stronger low speed response. If so that would point to an internal blockage.

Start w/ fresh plugs, replace inline fuel filter if equipped,clean & oil air filter, or replace w/ new oiled filter,check carb. boots for cracks or tears causing air leaks,check coolant condition & level,next adjust intake & exhaust valve tappet clearance to specs.,make sure fuel is fresh start & warm up bike & now synchronize the carbs using carb. synch. vacuum guage set.if bike still runs bad at this point take compression test,also you would want to change carb needles and main jets if you have replaced stock exhaust system,check & clean carbs when rejetting.actually do compression test 1st to give youtop end motor condition.