Buy Calgon Water Softener & More | drugstore.com
There are other places as well.
Calgon Water Softener has a chemical that coats the walls of the tank making it "slick" and stuff is reluctant to stick to it. Tank flushes cleaner.
The Laundry (or dish wash) soap is to help keep crud in suspension.
The 3-5 gallons of water in the black tank keeps solids moving around so it never gets a chance to pile up.
NEVER use anything with FABRIC softener.
It is a wax that coats the walls of the tank and makes your sensors unreliable.
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