Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3x2) +  66x) +  60

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6x² + 66x + 60  =   6 • (x² + 11x + 10) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² + 11x + 10 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +11x  its coefficient is  11 .
The last term, "the constant", is  +10 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 10 = 10 

Step-2 : Find two factors of  10  whose sum equals the coefficient of the middle term, which is   11 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  10 
                     x² + 1x + 10x + 10

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x+1)
              Add up the last 2 terms, pulling out common factors :
                    10 • (x+1)
Step-5 : Add up the four terms of step 4 :
                    (x+10)  •  (x+1)
             Which is the desired factorization

Final result :

  6 • (x + 10) • (x + 1)