Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5x2 -  17x) -  12

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²-17x-12 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -17x  its coefficient is  -17 .
The last term, "the constant", is  -12 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -12 = -60 

Step-2 : Find two factors of  -60  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,  -20  and  3 
                     5x² - 20x + 3x - 12

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

Final result :

  (x - 4) • (5x + 3)