Selling it yourself is the best, trading it in is the easiest.
You owe 13, they want to give you 14(and sell it for 17), but by dealing with the tire kickers, you could pull down 15-16. Dealers are looking at how much they can buy or sell your car at auction and overall profit out of the entire deal.
You negotiate your price on the Mustang (probably not a lot of room) then negotiate your trade. A salesperson should know that you're trading it in anyways.