When p2 – 4p is subtracted from p2 + p – 6, the result is 5p-6 To get p – 9, subtract

[tex] (p^{2} + p - 6) - (x) = p - 9 [/tex] is what is asked.

So all you need to do is a value that will result to p - 9.

x = [tex] (p^{2} + p - 6) - p + 9 [/tex]  To isolate x we just transpose the values from the other side of the equation and do the opposite operation. 

Combine like terms and just copy the terms that do not have similar expressions:

p will cancel out because p - p = 0
-6 and + 9  will come together because they are like terms: -6 + 9 = 3 
[tex] p^{2} [/tex] does not have a pair so it will remain as is. you will be left with:

[tex] p^{2} + 3[/tex]

Let us check:

   [tex]p^{2} + p - 6[/tex]
-  [tex]p^{2} + 0 + 3 [/tex]  
----------------------------
   [tex]0 + p - 9[/tex]    or [tex]p -9[/tex]