Answer
$x=\left\{ -3,1 \right\}$
Work Step by Step
Using the properties of equality, the given expression, $
3x^2-2x=9-8x
,$ is equivalent to
\begin{array}{l}\require{cancel}
3x^2-2x+8x-9=0
\\\\
3x^2+6x-9=0
.\end{array}
Factoring the above equation, $
3x^2+6x-9=0
,$ results to
\begin{array}{l}\require{cancel}
3(x^2+2x-3)=0
\\\\
x^2+2x-3=0
\\\\
(x+3)(x-1)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(x+3)(x-1)=0
,$ are
\begin{array}{l}\require{cancel}
x+3=0
\\\\
x=-3
,\\\\\text{OR}\\\\
x-1=0
\\\\
x=1
.\end{array}
Hence, $
x=\left\{ -3,1 \right\}
.$