There are many ways to answer your question depending on the interpretation of the reasons you are asking.

Strangely, you have not asked how does one come with the two equations in the first place.

There is no mysticism in there, the appearances nonwit'standing. I am just back from a vacation which I used to catch up with some reading. Ernest Hemingway had a rule of writing regularly and, if nothing came to mind, to force out a first sentence, and proceed in this manner until the story began compsing itself in his mind. Ray Bradbury used a list of random words to the same purpose. He would pick words frm a dictionary and then try ordering them in a meaningful sentence or bringing a meaningful recollection from his past.

The point is, in order to produce, you have to do something. There is no assurance that your efforts will bear fruit, let alone bear fruit immediately. But you have to try. And if something does not work you try something else. There is simply no other way. In time, you may develop intuition that will help you with picking up more promising venues to reach the solution.

When one writes down a proof one ignores the many failed attempts that led nowhere. This must be understood. Otherwise, the story would be too long.

So, to answer your question, I added two equations because this did the trick. Multiplying them led nowhere.