Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5x2 +  2x) -  3

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²+2x-3 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  +2x  its coefficient is  2 .
The last term, "the constant", is  -3 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -3 = -15 

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is   2 .

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

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (5x-3)
              Add up the last 2 terms, pulling out common factors :
                     1 • (5x-3)
Step-5 : Add up the four terms of step 4 :
                    (x+1)  •  (5x-3)
             Which is the desired factorization

Final result :

  (5x - 3) • (x + 1)