To solve the equation \( 15x^4 - 15x^2 = 0 \), follow these steps:

1. **Factor out the common term:**
   \[
   15x^2(x^2 - 1) = 0
   \]
   Here, \( 15x^2 \) is the common factor.

2. **Set each factor to zero:**
   \[
   15x^2 = 0 \quad \text{or} \quad x^2 - 1 = 0
   \]

3. **Solve each equation separately:**
   - For \( 15x^2 = 0 \):
     \[
     x^2 = 0
     \]
     Taking the square root of both sides:
     \[
     x = 0
     \]

   - For \( x^2 - 1 = 0 \):
     \[
     x^2 = 1
     \]
     Taking the square root of both sides:
     \[
     x = \pm 1
     \]

4. **Write down the solutions:**
   The solutions to the equation are \( x = 0, 1, \) and \( -1 \).

### Final Answer:
The values of \( x \) that satisfy the equation are \( x = 0, 1, \) and \( -1 \).

Would you like more details or have any questions about this solution?

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**Tip:** Always check for common factors first when solving polynomial equations, as it simplifies the process.

Learn how to solve the polynomial equation 15x^4 - 15x^2 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomial equations, factoring, and quadratic equations. Suitable for students in Grades 9-12.

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