Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (7m2 +  31m) -  20

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  7m²+31m-20 

The first term is,  7m²  its coefficient is  7 .
The middle term is,  +31m  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,  -4  and  35 
                     7m² - 4m + 35m - 20

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

Final result :

  (7m - 4) • (m + 5)