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One extra thought about why this is important, conceptually, as a technique.

Rawr. This is a first pass at a description of *the* most generic equation-solving technique I know. It actually applies to formulas sometimes too. Perhaps someone else can give better examples across more fields. But I noticed that this fundamental mathematical technique -- manipulating the equation until it's in a "solved" pattern -- didn't have a page yet. It's wildly important; a vast number of methods consist of just making logically equivalent transformations until you have a form which looks like something someone else already solved.

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