Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2a2 -  9a) -  18

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2a²-9a-18 

The first term is,  2a²  its coefficient is  2 .
The middle term is,  -9a  its coefficient is  -9 .
The last term, "the constant", is  -18 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -18 = -36 

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -9 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  3 
                     2a² - 12a + 3a - 18

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2a • (a-6)
              Add up the last 2 terms, pulling out common factors :
                    3 • (a-6)
Step-5 : Add up the four terms of step 4 :
                    (2a+3)  •  (a-6)
             Which is the desired factorization

Final result :

  (a - 6) • (2a + 3)