Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5x2 -  34x) -  7

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²-34x-7 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -34x  its coefficient is  -34 .
The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -7 = -35 

Step-2 : Find two factors of  -35  whose sum equals the coefficient of the middle term, which is   -34 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -35  and  1 
                     5x² - 35x + 1x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :
                    5x • (x-7)
              Add up the last 2 terms, pulling out common factors :
                     1 • (x-7)
Step-5 : Add up the four terms of step 4 :
                    (5x+1)  •  (x-7)
             Which is the desired factorization

Final result :

  (x - 7) • (5x + 1)