Answer
$(-\infty, 0] \cup [\frac{2}{3}, +\infty)$
Refer to the image below for the graph.
Work Step by Step
First step is to find the zeros of each factor.
To find value of $x$ that will make each factor equal to zero, equate each factor to zero then solve each equation:
$\begin{array}{ccc}
&x=0 &\text{ or } &2-3x=0
\\&x=0 &\text{ or } &2=3x
\\&x=0 &\text{ or } &\frac{2}{3}=x
\end{array}$
Next step is to find the intervals.
The zeros $0$ and $\frac{2}{3}$ divide the number line into three intervals, namely:
$(-\infty, 0), (0, \frac{2}{3}), \text{ and } (\frac{2}{3}, +\infty)$.
$\bf\text{Make a table of signs}.$
(refer to the attached image below)
$\bf\text{Solve}$
From the table of signs, it can be seen that $x(2-3x)\le 0$ in the intervals $(-\infty, 0)$ and $(\frac{2}{3}, +\infty)$.
The inequality involves $\le$ therefore the endpoints $0$ and $\frac{2}{3}$ are part of the solution set.
Thus, the solution set is $(-\infty, 0] \cup [\frac{2}{3}, +\infty)$.
To graph this, plot solid dots at $0$ and $\frac{2}{3}$ then shade the region to the left of $0$ and the region to the right of $\frac{2}{3}$.
(refer to the attached image in the answer part above)
