Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22p2 -  3p) -  10

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4p²-3p-10 

The first term is,  4p²  its coefficient is  4 .
The middle term is,  -3p  its coefficient is  -3 .
The last term, "the constant", is  -10 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -10 = -40 

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   -3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  5 
                     4p² - 8p + 5p - 10

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

Final result :

  (p - 2) • (4p + 5)