Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (7x2 -  7x) -  140

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   7x² - 7x - 140  =   7 • (x² - x - 20) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - x - 20 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -20 

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

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   -1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  4 
                     x² - 5x + 4x - 20

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

Final result :

  7 • (x + 4) • (x - 5)