Solving Cubic Equations (With Origami)

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I am working on a project about Mathematics and Origami. I am working on a section about how origami can be used to solve cubic equations. This is the source I am looking at:
http://origami.ousaan.com/library/conste.html
I understand the proof they go on to explain about how the slope of the crease line is the solution to the general cubic equation. I am also interested in understanding how this is used to double the cube and trisect the angle which they go on to mention at the end. However, I am having difficulty filling in the missing gaps and understanding how to use this origami method to solve those equations given and how this tells us we can trisect the angle, and double the cube. Any help is much appreciated