Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  3a2) -  17a) -  10

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -3a² - 17a - 10  =   -1 • (3a² + 17a + 10) 

Trying to factor by splitting the middle term

 3.2     Factoring  3a² + 17a + 10 

The first term is,  3a²  its coefficient is  3 .
The middle term is,  +17a  its coefficient is  17 .
The last term, "the constant", is  +10 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 10 = 30 

Step-2 : Find two factors of  30  whose sum equals the coefficient of the middle term, which is   17 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  15 
                     3a² + 2a + 15a + 10

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

Final result :

  (-3a - 2) • (a + 5)