Answer
$\left\{-3,\dfrac{1}{3}\right\}$
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
3x^2=3-8x
,$ is equivalent to
\begin{align*}
3x^2+8x-3&=0
.\end{align*}
Using factoring of trinomials, the equation above is equivalent to
\begin{align*}
(x+3)(3x-1)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable, then
\begin{array}{l|r}
x+3=0 & 3x-1=0
\\
x=-3 & 3x=1
\\\\
& x=\dfrac{1}{3}
.\end{array}
Hence, the solution set of the equation $
3x^2=3-8x
$ is $\left\{-3,\dfrac{1}{3}\right\}$.
