x2- 4x -21 has 2 factors
which by the FOIL method is x2 +3x -7x -21
when y=0, the x-intercepts are x=7 and x=-3
just set each factor equal to zero: x-7=0, so x=7; x+3=0, so x=-3
factoring is trial and error, but if there are easy integer factors, they will involve factors of the constant term which is 21. There are only two factors, 7 and 3. Then just make sure the signs are right. Since -4x has a negative coefficient, you want the larger number, the 7 to be negative and the 3 positive.