Solve the inequality $f(x)> 0$, where $f(x)=x^{2}(x+3)$, by using the graph of the function.
The solution set for $f(x)> 0$ is (Type your answer in interval notation.)

Step 1 ：Given the inequality $f(x)>0$, where $f(x)=x^{2}(x+3)$, we are looking for the values of $x$ where the function $f(x)$ is positive.

Step 2 ：The function $f(x)=x^{2}(x+3)$ is a cubic function and its graph will cross the x-axis at the roots of the equation $f(x)=0$. The roots of the equation are $x=0$ and $x=-3$.

Step 3 ：We can divide the number line into three intervals based on these roots: $(-\infty, -3)$, $(-3, 0)$, and $(0, \infty)$. We can then test a number from each interval to see if the function is positive or negative in that interval.

Step 4 ：For the interval $(-\infty, -3)$, we can test $x=-4$. For the interval $(-3, 0)$, we can test $x=-1$. For the interval $(0, \infty)$, we can test $x=1$.

Step 5 ：The function $f(x)$ is negative for $x$ in the interval $(-\infty, -3)$ and positive for $x$ in the intervals $(-3, 0)$ and $(0, \infty)$.

Step 6 ：Therefore, the solution set for the inequality $f(x)>0$ is $(-3, 0) \cup (0, \infty)$.

Step 7 ：\(\boxed{\text{The solution set for the inequality } f(x)>0 \text{ is } (-3, 0) \cup (0, \infty)}\)