Physics heat loss = heat gain question

Question

a hot 100 g iron rivet at 500 C is dropped into a bucket with 500 g of mercury at 20 C, no heat is lost, what is the final temperature?

So the equation sets up as

(.1kg)(448 J/KgC)(500-Tf) = (.5 kg)(138 J/kgC)(Tf-20 C)

How do you isolate the Tf? I thought you could multiply the #'s you know out and then get a number - a number times Tf?

Answer 1

44.8(500 - Tf) = (69)(Tf - 20)

22400 - 44.8Tf = 69Tf - 1380

2240+1380 = 69Tf + 44.8Tf

23780 = 113.8Tf

208 = Tf