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Why can the general quintic be transformed to $v^5-5\beta v^3+10\beta^2v-\beta^2 = 0$?

It took almost 20 long years (I first found the quintic back in April 2006), but I finally have the answer. Given the two similar one-parameter forms, $$u^5-10\alpha u^3+45\alpha^2u-\alpha^2 = 0\tag1$ …
Tito Piezas III's user avatar