Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5x2 +  26x) +  5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²+26x+5 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  +26x  its coefficient is  26 .
The last term, "the constant", is  +5 

Step-1 : Multiply the coefficient of the first term by the constant   5 • 5 = 25 

Step-2 : Find two factors of  25  whose sum equals the coefficient of the middle term, which is   26 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  25 
                     5x² + 1x + 25x + 5

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

Final result :

  (5x + 1) • (x + 5)