x³-9x = 0

To solve the equation \( x^3 - 9x = 0 \), we can start by factoring the expression.

1. Factor out \( x \):

   \[ x(x^2 - 9) = 0 \]

2. Recognize that \( x^2 - 9 \) is a difference of squares, which can be factored further:

   \[ x(x - 3)(x + 3) = 0 \]

3. Set each factor equal to zero:

   • \( x = 0 \)
   • \( x - 3 = 0 \) ⟹ \( x = 3 \)
   • \( x + 3 = 0 \) ⟹ \( x = -3 \)

Thus, the solutions to the equation \( x^3 - 9x = 0 \) are:

\[ x = 0, \quad x = 3, \quad x = -3 \]