Answer:

9p2-5p-4=0  

Two solutions were found :

p = -4/9 = -0.444

p = 1

Step-by-step EXPLANATION:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "p2"   was replaced by   "p^2".  

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (32p2 -  5p) -  4  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  9p2-5p-4  

The first term is,  9p2  its coefficient is  9 .

The middle term is,  -5p  its coefficient is  -5 .

The last term, "the constant", is  -4  

Step-1 : Multiply the coefficient of the first term by the constant   9 • -4 = -36  

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -5 .

     -36    +    1    =    -35  

     -18    +    2    =    -16  

     -12    +    3    =    -9  

     -9    +    4    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  4  

                    9p2 - 9p + 4p - 4

Step-4 : Add up the first 2 terms, pulling out like factors :

                   9p • (p-1)

             Add up the last 2 terms, pulling out common factors :

                   4 • (p-1)

Step-5 : Add up the FOUR terms of step 4 :

                   (9p+4)  •  (p-1)

            Which is the desired factorization

Equation at the end of step  2  :

 (p - 1) • (9p + 4)  = 0