I had got to this point- Mb + Mc = b - c subtract b, and Mc from both sides
Mb - b = - Mc - c multiply both sides by - 1 <---- Was skipping this part
was getting M = c(1-m)/(m+1)
When that didn't work I started racking my brain and then overlooking these steps and was becoming a brain drain cycle.
b - Mb = Mc + c factor both sides
b( 1 - M) = c ( M + 1) divide both sides by (1 - M)
Thanks! Rereading a couple times to get this to stick