4z^7 (8z^11 + 2z^4 + 3) = 0
I am assuming this is 32z^18 + 8z^11 + 12z^7.
The highest exponent you can factor from each of the terms is z^7 and the highest constant is 4 (as it is a factor of 32, 8, and 12).
Write this like:
4z^7 (8z^11 + 2z^4 + 3) = 0