Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((5•7x2) -  22x) +  3

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  35x²-22x+3 

The first term is,  35x²  its coefficient is  35 .
The middle term is,  -22x  its coefficient is  -22 .
The last term, "the constant", is  +3 

Step-1 : Multiply the coefficient of the first term by the constant   35 • 3 = 105 

Step-2 : Find two factors of  105  whose sum equals the coefficient of the middle term, which is   -22 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  -7 
                     35x² - 15x - 7x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :
                    5x • (7x-3)
              Add up the last 2 terms, pulling out common factors :
                     1 • (7x-3)
Step-5 : Add up the four terms of step 4 :
                    (5x-1)  •  (7x-3)
             Which is the desired factorization

Final result :

  (7x - 3) • (5x - 1)