Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((((5•(x2))-2)+10x)+7x2)-15x
 Step  2  :

Equation at the end of step  2  :

  (((5x2 -  2) +  10x) +  7x2) -  15x

Step  3  :

Trying to factor by splitting the middle term

 3.1     Factoring  12x²-5x-2 

The first term is,  12x²  its coefficient is  12 .
The middle term is,  -5x  its coefficient is  -5 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -2 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3 
                     12x² - 8x + 3x - 2

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

Final result :

  (3x - 2) • (4x + 1)