Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3q2) +  34q) -  28

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   12q² + 34q - 28  =   2 • (6q² + 17q - 14) 

Trying to factor by splitting the middle term

 3.2     Factoring  6q² + 17q - 14 

The first term is,  6q²  its coefficient is  6 .
The middle term is,  +17q  its coefficient is  17 .
The last term, "the constant", is  -14 

Step-1 : Multiply the coefficient of the first term by the constant   6 • -14 = -84 

Step-2 : Find two factors of  -84  whose sum equals the coefficient of the middle term, which is   17 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  21 
                     6q² - 4q + 21q - 14

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2q • (3q-2)
              Add up the last 2 terms, pulling out common factors :
                    7 • (3q-2)
Step-5 : Add up the four terms of step 4 :
                    (2q+7)  •  (3q-2)
             Which is the desired factorization

Final result :

  2 • (3q - 2) • (2q + 7)