Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  (3•5k2)) -  5k) +  50

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -15k² - 5k + 50  =   -5 • (3k² + k - 10) 

Trying to factor by splitting the middle term

 3.2     Factoring  3k² + k - 10 

The first term is,  3k²  its coefficient is  3 .
The middle term is,  +k  its coefficient is  1 .
The last term, "the constant", is  -10 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -10 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  6 
                     3k² - 5k + 6k - 10

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

Final result :

  -5 • (3k - 5) • (k + 2)