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