I guess this is f(x)=x²+2x-24 which factorises: f(x)=(x+6)(x-4), so the zeroes are when x+6=0 or x-4=0, that is, x=-6 and x=4.
To understand how to factorise, we need to look at the constant term and write down all its factors: 24=1×24=2×12=3×8=4×6. Now we look at the sign of the constant term. If it’s positive we look at the sum of the factors, and if it’s negative, their difference. In this case it’s negative so we take each pair of factors and work out the difference: 23, 10, 5 and 2. Now we look at the x coefficient. Does it match any of these differences? Yes. It matches the difference between factors 4 and 6. Now we look at the sign of the x term and we place that sign in front of the larger factor, which is 6. That gives us factor x+6. The opposite sign is needed for the other factor, so we have x-4. Now that we have both factors we can easily work out the zeroes.