If you're wondering how to factorise this, then you need to think of two numbers that:
-> Multiply together and give you -6
-> Add together to give you -1
Eventually you can do it in your head, but for now it's probably easiest to write down all the whole numbers that multiply together to give you -6;
-1x6 = -6 1x-6 = -6
-2x3 = -6 2x-3 = -6
Now from these numbers which ones add together to give you negative one?
-3 + 2 = -1
So the two numbers you needed are 2 and -3.
Therefore it factorises into \(z^2-z-6 = (z+2)(z-3)\).