@deprecated_ii @warmbeverageenjoyer @LukeAlmighty OK, here I have a mathematician explaining this exact equation in a way that's easier than what I would do. And I'll use it because he reached the same conclusion as me, so I have confirmation bias.
https://invidious.varishangout.net/watch?v=URcUvFIUIhQBut note that he doesn't say anything about the distributive property, because it really doesn't fit here. Saying that 2(1+2) is it's own equation that must be solved separately is not true, because there is nothing saying it is. You are assuming that 2(1+2) is just a 6 that was split, instead of being a equation that was reached through the insertion of numbers into variables or through the solving of previous equations.
Note that I had a wrong assumption in my last post, because I was taking a look at my college algebra books, and even in algebra you have a liberal use of parenthesis to avoid this kind of confusion.
6/2a is completely different from 6/(2a), wherein the first one is seen as
6
__ a
2
and the second is seen as
6
__
2a
(the formatting is terrible, but I think it can be understood).