There are three basic strategies that can be used to finance a franchise business startup. The first is to use your own money, accumulated over your lifetime, as the investment capital you need.  The second is to use assets you've acquired over your life as collateral in order to borrow the money you need from a lender that makes business startup loans. These are by far the two easiest strategies to employ, but I'm guessing from the tone of your question that neither of these strategies is going to work for you.

If you don't have the money you need or the assets to enable you to secure a loan, then you'll need an angel.  In my experience, private equity firms invest in existing companies with an established track record, so that approach is probably not going to work.  What you need to do is find a person (typically a relative or known business associate rather than a stranger) who is willing to take a risk on you because of the confidence he or she has in your ability.

While that's not easy to do, it is possible.  As a final note, expect to pay a substantially higher amount for capital you access in this manner, since angels usually require a significant equity stake as well as interest in exchange for advancing money into a startup.

Good luck!