How do you factor #n^2+8n=12#?
To be technically accurate (at least as I was taught) you factor expressions not equations.
I will assume that what you really want to do is find solutions for the given equation
(and then re-write the equation as a pair of factors equal to zero).
There are several ways to approach this:
trial and error;
quadratic formula for roots; or
completion of the square.
By completion of the square
Re-expressing the original equation as a pair of factors equal to zero