Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 -  27x) -  7

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4x²-27x-7 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  -27x  its coefficient is  -27 .
The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -7 = -28 

Step-2 : Find two factors of  -28  whose sum equals the coefficient of the middle term, which is   -27 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -28  and  1 
                     4x² - 28x + 1x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :
                    4x • (x-7)
              Add up the last 2 terms, pulling out common factors :
                     1 • (x-7)
Step-5 : Add up the four terms of step 4 :
                    (4x+1)  •  (x-7)
             Which is the desired factorization

Final result :

  (x - 7) • (4x + 1)