Answer
$x=\{ 0,36 \}$
Work Step by Step
Squaring both sides of the given equation, $
6\sqrt{x}=x
,$ results to
\begin{array}{l}\require{cancel}
6\sqrt{x}=x
\\\\
\left( 6\sqrt{x} \right)^2=(x)^2
\\\\
36x=x^2
\\\\
0=x^2-36x
\\\\
x^2-36x=0
.\end{array}
Factoring the $GCF=x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x^2-36x=0
\\\\
x(x-36)=0
.\end{array}
Equating each factor to zero (Zero Product Property), the solutions are
\begin{array}{l}\require{cancel}
x=0
\\\\\text{OR}\\\\
x-36=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x=0
\\\\\text{OR}\\\\
x-36=0
\\\\
x=36
.\end{array}
Upon checking, both solutions satisfy the original equation. Hence, $
x=\{ 0,36 \}
.$
