FOIL out (11x + 1)(ax + b)
          11ax2 + 11bx + 1ax + b

Factor out x from the middle two terms:

          11ax2 + (11b+a)x + b

Compare that with

            cx2 - 74x - 7

Those must equal to each other, so we set the corresponding
terms equal to each other:

Setting first terms equal:

11ax2 = cx2
  11a = c    

Setting second terms equal:

(11b+a)x = -74x
   11b+a = -74
  
Setting third terms equal:

       b = -7 

So we have the system of three equations:



Substitute b=-7 from the third equation into the second 
equation:

11(-7)+a = -74
   -77+a = -74
       a = 3

Substitute in the first:

    11a = c 
  11(3) = c
     33 = c

Edwin