<s>[INST] Solution to cubic inequality How do I find the solutions to this equation?  $$(3x^3)-(14x^2)-(5x) \leq 0$$
 [/INST] Step 1. Find the roots of the cubic equation $3x^3-14x^2-5x=0$.
$$
\begin{align*}
x(3x^2-14x-5)&=0\\
x(3x+1)(x-5)&=0\\
x&=0\quad\text{or}\\
x&=-\frac{1}{3}\quad\text{or}\\
x&=5
\end{align*}
$$
Step 2. Draw a sign table for $P=3x^3-14x^2-5x$.

Step 3: From your sign table, you can see that for $x\in(-\infty,-\frac{1}{3}]\cup[0,5]$, $P\leq0$.
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