I need to prepare for a math exam, however I haven't looked at anything resembling an equation in 10 years. I would appreciate any help you can provide, as I have lots of catch-up to do.

$\displaystyle

^{n+3} C _{n}~-~^{n+2} C _{n-1}~=~15(n+1)

$

How can I findn?

Probably I should use Newton's binomial, but I can't figure out how.