Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5k2 +  75k) +  270

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   5k² + 75k + 270  =   5 • (k² + 15k + 54) 

Trying to factor by splitting the middle term

 3.2     Factoring  k² + 15k + 54 

The first term is,  k²  its coefficient is  1 .
The middle term is,  +15k  its coefficient is  15 .
The last term, "the constant", is  +54 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 54 = 54 

Step-2 : Find two factors of  54  whose sum equals the coefficient of the middle term, which is   15 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  6  and  9 
                     k² + 6k + 9k + 54

Step-4 : Add up the first 2 terms, pulling out like factors :
                    k • (k+6)
              Add up the last 2 terms, pulling out common factors :
                    9 • (k+6)
Step-5 : Add up the four terms of step 4 :
                    (k+9)  •  (k+6)
             Which is the desired factorization

Final result :

  5 • (k + 9) • (k + 6)