Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3x2) -  21x) -  45

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6x² - 21x - 45  =   3 • (2x² - 7x - 15) 

Trying to factor by splitting the middle term

 3.2     Factoring  2x² - 7x - 15 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  -7x  its coefficient is  -7 .
The last term, "the constant", is  -15 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -15 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -7 .

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

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

Final result :

  3 • (x - 5) • (2x + 3)