Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3e2 +  3e) -  18

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3e² + 3e - 18  =   3 • (e² + e - 6) 

Trying to factor by splitting the middle term

 3.2     Factoring  e² + e - 6 

The first term is,  e²  its coefficient is  1 .
The middle term is,  +e  its coefficient is  1 .
The last term, "the constant", is  -6 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6 

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  3 
                     e² - 2e + 3e - 6

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

Final result :

  3 • (e + 3) • (e - 2)