Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5p2 -  p) -  18

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5p²-p-18 

The first term is,  5p²  its coefficient is  5 .
The middle term is,  -p  its coefficient is  -1 .
The last term, "the constant", is  -18 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -18 = -90 

Step-2 : Find two factors of  -90  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,  -10  and  9 
                     5p² - 10p + 9p - 18

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

Final result :

  (p - 2) • (5p + 9)