Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3•5x2) +  4x) -  8

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   60x² + 4x - 8  =   4 • (15x² + x - 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  15x² + x - 2 

The first term is,  15x²  its coefficient is  15 .
The middle term is,  +x  its coefficient is  1 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   15 • -2 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  6 
                     15x² - 5x + 6x - 2

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

Final result :

  4 • (3x - 1) • (5x + 2)