Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  (2•5b2)) +  14b) -  4

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -10b² + 14b - 4  =   -2 • (5b² - 7b + 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  5b² - 7b + 2 

The first term is,  5b²  its coefficient is  5 .
The middle term is,  -7b  its coefficient is  -7 .
The last term, "the constant", is  +2 

Step-1 : Multiply the coefficient of the first term by the constant   5 • 2 = 10 

Step-2 : Find two factors of  10  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,  -5  and  -2 
                     5b² - 5b - 2b - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    5b • (b-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (b-1)
Step-5 : Add up the four terms of step 4 :
                    (5b-2)  •  (b-1)
             Which is the desired factorization

Final result :

  -2 • (b - 1) • (5b - 2)