Having now understood how this all works from the Khan Academy explanation, the real magic of all of this are these two things: 1) math that’s hard to do backw

Having now understood how this all works from the Khan Academy explanation, the real magic of all of this are these two things: 1) math that’s hard to do backwards 2) the transitive property of mathematics. Given #1 is basically arbitrary, I think it can be hand-waved in service of explaining the process, which only works because of that transitive property, which I think the person you replied to did a decent job of relating. In these explanations, people are getting hung up on the literal nuts and bolts steps, but simply understanding that we can send parts of a complete equation to each other and let the rules of math sort it out really clarifies the point.