Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•5x2) +  3x) -  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  10x²+3x-1 

The first term is,  10x²  its coefficient is  10 .
The middle term is,  +3x  its coefficient is  3 .
The last term, "the constant", is  -1 

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

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  5 
                     10x² - 2x + 5x - 1

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

Final result :

  (5x - 1) • (2x + 1)