75F - 201.5Fy = -201.5y + 111.5

have we simply added 75F and subtracted 201.5Fy to/from both sides of the equation here? ie making sure the equation stays "balanced" or whatever the term is?
Yes, it's correct the ultimate goal is to isolate F so we do what you said to get all the terms containing a F on one side of the equation and all the ones that don't on the other side.

F(75 - 201.5y) = -201.5y + 111.5

no idea what's happened at this point.
Again the goal is to isolate F and this is just stemming from the distributive property of multiplication:
A*(B+C) = A*B + A*C
or with numbers for example:
you can see that 3*(5+4) = 3*9 = 27, right.
But that is also the same as 3*5 + 3*4 = 15 + 12 = 27, right?
Spoon also explains it here (part 5): http://www.flopturnriver.com/pokerfo...ad-180192.html

F = (-201.5y + 111.5)/(75 - 201.5y)

no idea whats happened here because i need to know what happened in the last step.
Well explained by Mr Bucket above, we want to get F alone on one side, so we divide both sides by 75 -201.5y