Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5x2 -  13x) -  6

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²-13x-6 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -13x  its coefficient is  -13 .
The last term, "the constant", is  -6 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -6 = -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 
                     5x² - 15x + 2x - 6

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

Final result :

  (x - 3) • (5x + 2)