Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x2 -  8x) +  5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3x²-8x+5 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  -8x  its coefficient is  -8 .
The last term, "the constant", is  +5 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 5 = 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 
                     3x² - 5x - 3x - 5

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

Final result :

  (3x - 5) • (x - 1)