Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3c2) +  5c) -  2

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  12c²+5c-2 

The first term is,  12c²  its coefficient is  12 .
The middle term is,  +5c  its coefficient is  5 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -2 = -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 
                     12c² - 3c + 8c - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3c • (4c-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (4c-1)
Step-5 : Add up the four terms of step 4 :
                    (3c+2)  •  (4c-1)
             Which is the desired factorization

Final result :

  (4c - 1) • (3c + 2)