I have never used Dawn dish soap. I use yeast and peroxide in my holding tanks to clean them out while going down the road and while it is filling up when camping. It gets rid of solids and smells in tanks. You don't have to wonder if the black tank emptied out all of it's contents. If you want to completely clean out your black water tank, with tank empty, add 4 ounces of yeast, 10 ounces of peroxide and 1 gallon of water. As you are going down the road it is sloshing all over the tank and cleaning it good.
A 32 ounce of peroxide at Walmart is $1.00. By all means put water in tank first.The yeast and peroxide both eliminate the solids, not the paper. If you want to see how this works, sit on commode, have a bowel movement, pour in 1 ounce of yeast and let sit in bowl for an hour or so with lid down. The solid will turn into a soft mush. Flush and decide if it is worth trying.Yeast will keep septic tanks clean and helps eliminate solids in tank and you don't have to pump a septic tank our so often.
This is the best way to keep your tanks clean and odor free.