How can I finance my business with equity?
Financing your new business with equity makes sense when you want to share the risk, rather than taking on all the risk yourself by obtaining a loan. The risk is shared because your investors become co-owners, and each offers some money or services which they risk losing if the business fails. In exchange for taking this risk, your investors become co-owners of the company.
Your investors will typically want some type of protection, so that they know only their invested amount of money is at risk. You can offer this protection by setting your business up as a limited partnership (and making those investors limited partners), a corporation (and selling those investors stock, making them shareholders) or as an LLC (making the investors members of the LLC).
When you go the investment route, particularly if your business is a corporation, you also need to make sure that you follow and comply with any relevant federal and/or state securities laws.