Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5m2 +  35m) -  150

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   5m² + 35m - 150  =   5 • (m² + 7m - 30) 

Trying to factor by splitting the middle term

 3.2     Factoring  m² + 7m - 30 

The first term is,  m²  its coefficient is  1 .
The middle term is,  +7m  its coefficient is  7 .
The last term, "the constant", is  -30 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -30 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  10 
                     m² - 3m + 10m - 30

Step-4 : Add up the first 2 terms, pulling out like factors :
                    m • (m-3)
              Add up the last 2 terms, pulling out common factors :
                    10 • (m-3)
Step-5 : Add up the four terms of step 4 :
                    (m+10)  •  (m-3)
             Which is the desired factorization

Final result :

  5 • (m + 10) • (m - 3)