To solve the equation:

\[
2x^3 - 726x = 0
\]

1. **Factor out the common term:** Both terms contain an \( x \), so we can factor out \( 2x \):
   \[
   2x(x^2 - 363) = 0
   \]

2. **Set each factor to zero:** Now we have a product that equals zero, so each factor can be set to zero:
   \[
   2x = 0 \quad \text{or} \quad x^2 - 363 = 0
   \]

3. **Solve each equation separately:**

   - For \( 2x = 0 \):
     \[
     x = 0
     \]

   - For \( x^2 - 363 = 0 \):
     \[
     x^2 = 363
     \]
     \[
     x = \pm \sqrt{363}
     \]

     Calculating \( \sqrt{363} \approx 19.05 \), so:
     \[
     x = \pm 19.05
     \]

4. **Combine the solutions:**
   \[
   x = 0, \quad x \approx 19.05, \quad x \approx -19.05
   \]

### Final Answer
The solutions are:
\[
x = 0, \quad x \approx 19.05, \quad x \approx -19.05
\]

Would you like more details on the steps or have any questions?

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Here are 5 related questions for further practice:
1. How would you solve \( 3x^3 - 450x = 0 \)?
2. What is the solution to \( x^3 - 4x = 0 \)?
3. How can you solve \( 5x^4 - 500x = 0 \) by factoring?
4. What if the equation was \( x^3 - 726 = 0 \)? How would the approach differ?
5. How can you determine the nature of roots for similar equations?

**Tip:** When solving polynomial equations, look for common factors you can factor out first to simplify the equation.

Learn how to solve the polynomial equation 2x^3 - 726x = 0 by factoring and using the Zero Product Property. This step-by-step solution covers factoring techniques and solving equations for polynomial expressions. Ideal for high school students in Grades 9-10.

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