I had a slow-draining bath sink, plunger, no go.
Took off trap, tried to snake it, no go.
Finally tried Liquid Plumr "foaming pipe snake." Took two
applications, letting sit for six hours each, but it worked. About 9
months later, slow again, used pipe snake again. Once again took two
bottles. That was a couple of years ago.
Have septic system. They claim it is safe for it.
The safest solution is to hire a plumber to snake out the drain, but
$80 vs. $15....plus not having to wait around for the plumber, etc......