Factor the numerator.
What 2 numbers when multiplied equal 63*4=252 and when added equal -43?. Hmmmm...kind of rough, huh?.
Well, if we make a list and think a little we can find those numbers.
How about -36 and -7?. (-36)(-7)=252 and -36+(-7)=-43
\(\displaystyle 4x^{2}-36x-7x+63\)
Group and factor:
\(\displaystyle 4x^{2}-36x-7x+63\)
\(\displaystyle 4x(x-9)-7(x-9)\)
\(\displaystyle (4x-7)(x-9)\)
Now, I am sure you can finish.