Question

I am trying to understand what the purpose/application of factoring as in quadratics is.

Answer 1

There are several reasons why you would factor an quadratic equation, however, the first that comes to my mind is solving for roots or for the x-value(s).
Ex)
x^2-2x=-1
x^2-2x+1=0
If we factor:
(x-1)(x-1)=0
From this we can see that x=1, so that's our x-value for this equation.
You can double check that by plugging back in:
1-2+1=0 ... Check