How do you go about merging 2 businesses if 1 is a corporation and 1 is an LLC.?
You have two options:
1) Business 1 buys business 2. It doesn't matter which is which--the corporation can buy the LLC or vice versa. All that's necessary is that a majority of the ownership interest of business 2 sells their ownership interest to business 1. Once business 1 owns business 2, it can do with 2 as it wants: operate it as a fully separate unit; or fold all the back-office functions together while still using 2 as a consumer-facing brand; or phase out 2 altogether over time; etc.
2) Or business 1 can buy all the assets of business 2 (e.g. customer list, intellectual property, inventory, accounts receivable, equipment, etc.) and then business 2 can be shut down or dissolved.
Buying the actual business is useful if it has lots of contracts you wish to keep, lots of good will or name recognition, and/or may have claims it could assert in the future that the buying business would like to perhaps take advantage of.
Buying just the assets is better if business 2 has lots of obligations (whehter monetary or contractual) that business 1 does not want to take on.