Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (7a2 +  22a) +  3

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  7a²+22a+3 

The first term is,  7a²  its coefficient is  7 .
The middle term is,  +22a  its coefficient is  22 .
The last term, "the constant", is  +3 

Step-1 : Multiply the coefficient of the first term by the constant   7 • 3 = 21 

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   22 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  21 
                     7a² + 1a + 21a + 3

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (7a+1)
              Add up the last 2 terms, pulling out common factors :
                    3 • (7a+1)
Step-5 : Add up the four terms of step 4 :
                    (a+3)  •  (7a+1)
             Which is the desired factorization

Final result :

  (7a + 1) • (a + 3)