Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  2u2) -  u) +  21

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -2u² - u + 21  =   -1 • (2u² + u - 21) 

Trying to factor by splitting the middle term

 3.2     Factoring  2u² + u - 21 

The first term is,  2u²  its coefficient is  2 .
The middle term is,  +u  its coefficient is  1 .
The last term, "the constant", is  -21 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -21 = -42 

Step-2 : Find two factors of  -42  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,  -6  and  7 
                     2u² - 6u + 7u - 21

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2u • (u-3)
              Add up the last 2 terms, pulling out common factors :
                    7 • (u-3)
Step-5 : Add up the four terms of step 4 :
                    (2u+7)  •  (u-3)
             Which is the desired factorization

Final result :

  (3 - u) • (2u + 7)