Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•5x2) -  x) -  2

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  10x²-x-2 

The first term is,  10x²  its coefficient is  10 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   10 • -2 = -20 

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   -1 .

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

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

Final result :

  (2x - 1) • (5x + 2)