Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5x2 -  8x) +  3

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²-8x+3 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -8x  its coefficient is  -8 .
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   -8 .

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

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

Final result :

  (x - 1) • (5x - 3)