Solving for #p# means to "isolate" the variable, expressing it in terms of the others.

First of all, we observe that #4px+9py=p(4x+9y)#. This given, if we wanted to be particularly meticolous, we should observe that #(4x+9y)# must be non-zero, otherwise our equation would be #2x=0#, which can't be solved for #p#.

So, if our hypothesis holds, we can divide both sides by #(4x+9y)# (which is another reason why it should be non-zero), and obtain

#p=-{2x}/{4x+9y}#

which is exacly what we mean for "solving for #p#".