Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3p2 -  13p) -  10

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3p²-13p-10 

The first term is,  3p²  its coefficient is  3 .
The middle term is,  -13p  its coefficient is  -13 .
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   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  2 
                     3p² - 15p + 2p - 10

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

Final result :

  (p - 5) • (3p + 2)