I got stuck on a system of three equations
Subtract the first equation from the second $$ \tag{1}b(c^2 - 1) = 15$$ Subtract the second equation from the third $$ \tag{2} b(c^4 - c^2) = bc^2(c^2 - 1) = 60$$ Divide $(2)$ by $(1)$ $$ c^2 = 4$$ It's pretty straightforward from here on.