how many values of 'p' satisfy the equation: (log base5 p)^2 +log base5p (5/p)=1 ?

$$(log_5p)^2 + log_{5p}5/p = 1$$
$$= (log_5p)^2 + log_{5p}5 - log_{5p}(p) = 1$$
= $$(log_5p)^2 + \frac{1}{log_55p} - \frac{1}{log_p5p} = 1$$
= $$(log_5p)^2 + \frac{1}{1 + log_5p} - \frac{1}{1 + log_p5} = 1$$
Let $$log_5p = x $$
the equation becomes, $$x^2 + \frac{1}{1 + x} + \frac{1}{1 + 1/x} = 1$$
On, simplifying we get, $$ x^3 + x^2 + x -1 = 0$$
= x(x + 2)(x - 1) = 0
Thus, the values of x are 0,1 and -2.
The corresponding values of p are 1, 5 and 1/25. Thus, three values of p are possible.