My 2002 eclipse with 3.0 v6 idles rough and shuts off when hot when stopping

What is your question?

When I'm gear at idle the steering wheel vibrates and when hot and you stop it wants to shut off normally the idle is about 500 rpms. To keep it from shutting off when you stop you have to keep your foot on the gas to maintain about 1000 rpms to keep it running

What makes this problem better or worse?

it is worst when engine is hot. you stop at a stop light it will shut off if you don't hold your foot on the gas to keep the idle at 1000 rpms. it idles at about 500 rpms

How long has your 2002 Mitsubishi Eclipse had this problem?

a few weeks