Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3r2) -  23r) +  20

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  6r²-23r+20 

The first term is,  6r²  its coefficient is  6 .
The middle term is,  -23r  its coefficient is  -23 .
The last term, "the constant", is  +20 

Step-1 : Multiply the coefficient of the first term by the constant   6 • 20 = 120 

Step-2 : Find two factors of  120  whose sum equals the coefficient of the middle term, which is   -23 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  -8 
                     6r² - 15r - 8r - 20

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

Final result :

  (2r - 5) • (3r - 4)