Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((3•5q2) -  2q) -  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  15q²-2q-1 

The first term is,  15q²  its coefficient is  15 .
The middle term is,  -2q  its coefficient is  -2 .
The last term, "the constant", is  -1 

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

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is   -2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  3 
                     15q² - 5q + 3q - 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    5q • (3q-1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (3q-1)
Step-5 : Add up the four terms of step 4 :
                    (5q+1)  •  (3q-1)
             Which is the desired factorization

Final result :

  (3q - 1) • (5q + 1)