Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (7r2 -  55r) +  42

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  7r²-55r+42 

The first term is,  7r²  its coefficient is  7 .
The middle term is,  -55r  its coefficient is  -55 .
The last term, "the constant", is  +42 

Step-1 : Multiply the coefficient of the first term by the constant   7 • 42 = 294 

Step-2 : Find two factors of  294  whose sum equals the coefficient of the middle term, which is   -55 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -49  and  -6 
                     7r² - 49r - 6r - 42

Step-4 : Add up the first 2 terms, pulling out like factors :
                    7r • (r-7)
              Add up the last 2 terms, pulling out common factors :
                    6 • (r-7)
Step-5 : Add up the four terms of step 4 :
                    (7r-6)  •  (r-7)
             Which is the desired factorization

Final result :

  (r - 7) • (7r - 6)