Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3a2) -  13a) -  35

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  12a²-13a-35 

The first term is,  12a²  its coefficient is  12 .
The middle term is,  -13a  its coefficient is  -13 .
The last term, "the constant", is  -35 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -35 = -420 

Step-2 : Find two factors of  -420  whose sum equals the coefficient of the middle term, which is   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -28  and  15 
                     12a² - 28a + 15a - 35

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

Final result :

  (3a - 7) • (4a + 5)