Answer
$x=\left\{ 2,3 \right\}$
Work Step by Step
Using $x^{-a}=\dfrac{1}{x^a}$, the given equation, $
6p^{-2}-5p^{-1}+1=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{6}{p^2}-\dfrac{5}{p}+1=0
.\end{array}
Multiplying both sides by the $LCD=
p^2
,$ then the solution to the given equation is
\begin{array}{l}\require{cancel}
1(6)-p(5)+p^2(1)=0
\\\\
6-5p+p^2=0
\\\\
p^2-5p+6=0
\\\\
(p-3)(p-2)=0
\\\\
x=\left\{ 2,3 \right\}
.\end{array}
