A "drain bladder" or "sewer jetter bladder" ($10–20 at hardware stores).

After clearing the clog, flush 5 gallons of hot water once a month to prevent recurrence. If you have to repeat these methods every 2 weeks, you likely have tree roots or a broken pipe—a snake won’t fix that either.

Soap dissolves grease; hot water melts it so it can be flushed away.

A wet/dry shop vac with a 5+ gallon capacity and a long hose.

A heavy-duty mop head (string style) or a large rag wrapped around a sturdy broom handle. Duct tape.