Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3x2) -  8x) -  15

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  12x²-8x-15 

The first term is,  12x²  its coefficient is  12 .
The middle term is,  -8x  its coefficient is  -8 .
The last term, "the constant", is  -15 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -15 = -180 

Step-2 : Find two factors of  -180  whose sum equals the coefficient of the middle term, which is   -8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  10 
                     12x² - 18x + 10x - 15

Step-4 : Add up the first 2 terms, pulling out like factors :
                    6x • (2x-3)
              Add up the last 2 terms, pulling out common factors :
                    5 • (2x-3)
Step-5 : Add up the four terms of step 4 :
                    (6x+5)  •  (2x-3)
             Which is the desired factorization

Final result :

  (2x - 3) • (6x + 5)