Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (7x2 -  31x) -  20

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  7x²-31x-20 

The first term is,  7x²  its coefficient is  7 .
The middle term is,  -31x  its coefficient is  -31 .
The last term, "the constant", is  -20 

Step-1 : Multiply the coefficient of the first term by the constant   7 • -20 = -140 

Step-2 : Find two factors of  -140  whose sum equals the coefficient of the middle term, which is   -31 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -35  and  4 
                     7x² - 35x + 4x - 20

Step-4 : Add up the first 2 terms, pulling out like factors :
                    7x • (x-5)
              Add up the last 2 terms, pulling out common factors :
                    4 • (x-5)
Step-5 : Add up the four terms of step 4 :
                    (7x+4)  •  (x-5)
             Which is the desired factorization

Final result :

  (x - 5) • (7x + 4)