back firing and rough idle

Welcome to 2CarPros.

Is the back fire through the carburetor or exhaust? Have you checked for vacuum leaks which can cause this? How was the carburetor adjusted?

Here are a couple links you may find helpful:

https://www.2carpros.com/articles/engine-backfires-while-running

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

Also, are you certain that you have all ignition wires to the correct cylinders?

Let me know.

Joe