#### Answer

$(-\infty, -3.5] \cup [0, +\infty)$
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:
$\begin{array}{ccc}
&x=0 &\text{ or } &2x+7=0
\\&x=0 &\text{ or } &2x=-7
\\&x=0 &\text{ or } &x=-\frac{7}{2}
\\&x=0 &\text{ or } &x=-3.5
\end{array}$
Next step is to find the intervals.
The zeros $-3.5$ and $0$ divide the number line into three intervals, namely:
$(-\infty, -3.5), (-3.5, 0), \text{ and } (0, +\infty)$.
$\bf\text{Make a table of signs}.$
(refer to the attached image below)
$\bf\text{Solve}$
From the table of signs, it can be seen that $x(2x+7)\ge 0$ in the intervals $(-\infty, -3.5)$ and $(0, +\infty)$.
The inequality involves $ge$ therefore the endpoints $-3.5$ and $0$ are part of the solution set.
Thus, the solution set is $(-\infty, -3.5] \cup [0, +\infty)$.
To graph this, plot solid dots at $-3.5$ and $0$ then shade the region to the left of $-3.5$ and the region to the right of $0$.
(refer to the attached image in the answer part above)