The problem is to solve the equation $3x^3 - 27x = 0$ for $x$.

1. Problem Description

The problem is to solve the equation $3x^3 - 27x = 0$ for $x$.

2. Solution Steps

First, we can factor out a common factor of $3x$ from both terms:

$$3x(x^2 - 9) = 0$$

Next, we can further factor the term $x^2 - 9$ as a difference of squares:

$$x^2 - 9 = (x - 3)(x + 3)$$

So, the equation becomes:

$$3x(x - 3)(x + 3) = 0$$

Now, we set each factor equal to zero and solve for $x$:

$3x = 0 \implies x = 0$

$x - 3 = 0 \implies x = 3$

$x + 3 = 0 \implies x = -3$

3. Final Answer

The solutions are $x = 0$, $x = 3$, and $x = -3$.