Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (32x2 -  39x) -  30

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   9x² - 39x - 30  =   3 • (3x² - 13x - 10) 

Trying to factor by splitting the middle term

 3.2     Factoring  3x² - 13x - 10 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  -13x  its coefficient is  -13 .
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   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  2 
                     3x² - 15x + 2x - 10

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

Final result :

  3 • (x - 5) • (3x + 2)