Answer
$x\lt-5$
Work Step by Step
$3x^3\lt-15x^2\\3x^3+15x^2\lt0\\3x^2(x+5)\lt0$
The zeros from $3x^2(x+5)=0$: $x=0$ or $x+5=0\\x=-5$.
I use the real zeros to separate the real number line into three intervals:
$(-\infty,0)$, $(0,5)$, $(5,\infty)$.
I know select a test number in each interval found in the step above and evaluate the function on the left side of the inequality at each number to determine if the function is positive or negative. Refer to the table for this.
According to the table: $x\lt-5$ because the function is negative in this interval. Since the inequality is strict, the zeros are not included.
