Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3a2 +  30a) +  63

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3a² + 30a + 63  =   3 • (a² + 10a + 21) 

Trying to factor by splitting the middle term

 3.2     Factoring  a² + 10a + 21 

The first term is,  a²  its coefficient is  1 .
The middle term is,  +10a  its coefficient is  10 .
The last term, "the constant", is  +21 

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

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   10 .

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

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

Final result :

  3 • (a + 7) • (a + 3)