Answer
$y=\{ 0,49 \}$
Work Step by Step
Squaring both sides of the given equation, $
7\sqrt{y}=y
,$ results to
\begin{array}{l}\require{cancel}
7\sqrt{y}=y
\\\\
\left( 7\sqrt{y} \right)^2=(y)^2
\\\\
49y=y^2
\\\\
0=y^2-49y
\\\\
y^2-49y=0
.\end{array}
Factoring the $GCF=y,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
y^2-49y=0
\\\\
y(y-49)=0
.\end{array}
Equating each factor to zero (Zero Product Property), the solutions are
\begin{array}{l}\require{cancel}
y=0
\\\\\text{OR}\\\\
y-49=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
y=0
\\\\\text{OR}\\\\
y-49=0
\\\\
y=49
.\end{array}
Upon checking, both solutions satisfy the original equation. Hence, $
y=\{ 0,49 \}
.$
