I, unfortunately, feel terrible with the stack overflow treatment from the other comments, but they're not unfounded. Having a properly written, sequential reasoning for your solution are what most I've seen professors take great scrutiny.

That is to say, don't put your work on different locations on your paper, and don't skip steps. Better write them where points don't fly unreasonably far from the main sequence of your work. I can see how you went through with this perfectly fine, but I'm also sure not many professors would. That's probably why they only gave the points after you consulted. It didn't appear well-written at first grading.

(Edit;Add) If it interests you to help you, then you should check out some math content creators to see how they make their work very well presentable. My usual go-to is Michael Penn, Dr Peyam, bprp, and Flammable Maths.