<----- We transferred the -sr to the left side and it became +sr. This is exactly what happens when you move terms to the other side of the equals sign. You ALWAYS change their signs, and you do that whether you're transferring from left to right or right to left.
<----- The sr really is rs (due to that reflexive property of multiplication that says ab = ba).
<-------- We combined the two rs's because they're like terms.
<-------- Factor out the r from the 2rs and the -rt. (This is basically undistributing).
<------- Divide both sides by the quantity (2s - t). Now, you've got r by itself on the left and the expression on the right does NOT contain the r variable. That's what you want- to rewrite the equation as "r = something" such that the "something" does NOT include the r.