Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5x2 +  6x) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²+6x+1 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  +6x  its coefficient is  6 .
The last term, "the constant", is  +1 

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

Step-2 : Find two factors of  5  whose sum equals the coefficient of the middle term, which is   6 .

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

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 :
                     1 • (5x+1)
Step-5 : Add up the four terms of step 4 :
                    (x+1)  •  (5x+1)
             Which is the desired factorization

Final result :

  (5x + 1) • (x + 1)