For my A-Level Maths, I was taught a method for factorising quadratic equations; it'll seem complicated but I'll try to make the method as clear as I can.
So, if the equation is 2x² + 11x + 12...
You'll first want to separate the '11x' part into two additions.
To do this, multiply the 2 (the x² coefficient) with the 12 (the constant, without an x) = 24.
Then, see what two numbers
multiply to get 24, while also that
add to get 11 (the x coefficient). The two numbers here would be 8 and 3.
Thus, you write the equation as... 2x² + 8x + 3x + 12
With this new equation (where the x coefficient is merely split into two additions), divide it into two halves and factorise so that there is a common factor of each... 2x² + 8x + 3x + 12 will become... 2x(x + 4) + 3(x + 4)
The (x + 4) is the common factor here, so you can write the factorised equation as (2x + 3)(x + 4).
Yeah, I've explained this really badly and I'm certain that somebody will be able to explain this or another method far better - but oh well, it's one way!