Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 -  64x) +  252

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4x² - 64x + 252  =   4 • (x² - 16x + 63) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - 16x + 63 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -16x  its coefficient is  -16 .
The last term, "the constant", is  +63 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 63 = 63 

Step-2 : Find two factors of  63  whose sum equals the coefficient of the middle term, which is   -16 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -7 
                     x² - 9x - 7x - 63

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-9)
              Add up the last 2 terms, pulling out common factors :
                    7 • (x-9)
Step-5 : Add up the four terms of step 4 :
                    (x-7)  •  (x-9)
             Which is the desired factorization

Final result :

  4 • (x - 7) • (x - 9)