Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22k2 +  20k) -  96

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4k² + 20k - 96  =   4 • (k² + 5k - 24) 

Trying to factor by splitting the middle term

 3.2     Factoring  k² + 5k - 24 

The first term is,  k²  its coefficient is  1 .
The middle term is,  +5k  its coefficient is  5 .
The last term, "the constant", is  -24 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  8 
                     k² - 3k + 8k - 24

Step-4 : Add up the first 2 terms, pulling out like factors :
                    k • (k-3)
              Add up the last 2 terms, pulling out common factors :
                    8 • (k-3)
Step-5 : Add up the four terms of step 4 :
                    (k+8)  •  (k-3)
             Which is the desired factorization

Final result :

  4 • (k + 8) • (k - 3)