Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  5k2) -  22k) +  15

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -5k² - 22k + 15  =   -1 • (5k² + 22k - 15) 

Trying to factor by splitting the middle term

 3.2     Factoring  5k² + 22k - 15 

The first term is,  5k²  its coefficient is  5 .
The middle term is,  +22k  its coefficient is  22 .
The last term, "the constant", is  -15 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -15 = -75 

Step-2 : Find two factors of  -75  whose sum equals the coefficient of the middle term, which is   22 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  25 
                     5k² - 3k + 25k - 15

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

Final result :

  (3 - 5k) • (k + 5)