Answer
$x=\{-1,2\}$
Work Step by Step
Isolating the radical expression, the given expression is equivalent to
\begin{array}{l}\require{cancel}
x=\sqrt{3x+3}-1
\\\\
x+1=\sqrt{3x+3}
.\end{array}
Squaring both sides, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x+1=\sqrt{3x+3}
\\\\
(x+1)^2=(\sqrt{3x+3})^2
\\\\
(x)^2+2(x)(1)+(1)^2=3x+3
\\\\
x^2+2x+1=3x+3
\\\\
x^2+2x-3x+1-3=0
\\\\
x^2-x-2=0
.\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the equation above is equivalent to\begin{array}{l}\require{cancel}
x^2-x-2=0
\\\\
(x-2)(x+1)=0
.\end{array}
Equating each factor to zero (Zero Product Property) and solving for the variable, then the solutions are $
x=\{-1,2\}
.$
Upon checking, both solutions, $
x=\{-1,2\}
,$ satisfy the original equation.
