To solve the equation \( y^3 = 36y \), we can rearrange it:

1. Subtract \( 36y \) from both sides:

   \[
   y^3 - 36y = 0
   \]

2. Factor out \( y \):

   \[
   y(y^2 - 36) = 0
   \]

3. This gives us two factors: \( y = 0 \) and \( y^2 - 36 = 0 \).

4. Solve \( y^2 - 36 = 0 \):

   \[
   y^2 = 36
   \]
   \[
   y = 6 \quad \text{or} \quad y = -6
   \]

Thus, the solutions are:

\[
y = 0, \quad y = 6, \quad y = -6
\]

Would you like any further details or explanations? Here are some related questions you might consider:

1. How do you verify the solutions to the equation?
2. What are the graphical representations of these solutions?
3. Can this equation have complex solutions?
4. How can you apply similar methods to solve different polynomial equations?
5. What are the implications of factoring in solving polynomial equations?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they are valid.

Discover how to solve the equation y^3 = 36y with a detailed explanation of the factoring process and solutions. This guide covers fundamental algebra concepts suitable for students in Grades 8-10.

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