The "steps" are (1) to realize that 5 is a difference rather than a sum (and the reason we know this is the minus sign on the 24), and then (2) to think of two factors of 24 that differ by 5.

The only integer pairs that multiply to 24 are

1*24, 2*12, 3*8, 4*6,

and it's obvious that the only pair differing by 5 is the pair 3 and 8.

So now it's a matter of putting the correct signs in the binomials

(t +/- 3) and (t +/- 8). Their signs must be opposite in order to get -24, and the positive 5t must come from +8t - 3t rather than +3t - 8t. So the factors are:

(t - 3)(t + 8).