Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 -  8x) -  5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4x²-8x-5 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  -8x  its coefficient is  -8 .
The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -5 = -20 

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   -8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  2 
                     4x² - 10x + 2x - 5

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

Final result :

  (2x - 5) • (2x + 1)