This equation factorises: (2X+1)(X-4)=0, so X=-1/2 and X=4 is the solution. The Rational Zeros Theorem hints at the solutions by considering the factors of the coefficient of X^2 (2) and the constant term 4, that is 2*1 and 4*1 or 2*2. These give you an idea of what might go in the brackets with X, and it turns out that the theorem has covered the actual answer 2*1 and 1*4, which we can see in the brackets, 2X in the first bracket and X in the second, and 1 in the first bracket and 4 in the second.