To solve the equation \( x^2 \times 8 = x^3 \), follow these steps:

### Step 1: Simplify the equation
The equation is \( 8x^2 = x^3 \).

### Step 2: Move all terms to one side
Subtract \( x^3 \) from both sides of the equation to set it equal to zero:
\[
8x^2 - x^3 = 0
\]

### Step 3: Factor the equation
Factor out the common term \( x^2 \) from the equation:
\[
x^2(8 - x) = 0
\]

### Step 4: Solve for \( x \)
The equation \( x^2(8 - x) = 0 \) gives us two possible solutions:

1. \( x^2 = 0 \)  
   \[
   x = 0
   \]

2. \( 8 - x = 0 \)  
   \[
   x = 8
   \]

### Final Answer
The solutions are \( x = 0 \) and \( x = 8 \).

Would you like more details or have any questions? 

Here are 5 related questions to expand your understanding:

1. What would the solution be if the equation was \( 8x^2 = 2x^3 \)?
2. How would the solutions change if the equation were \( 8x^2 = x^4 \)?
3. What are the solutions to the equation \( 8x^2 - x^3 + 5 = 0 \)?
4. How do you factor quadratic equations like \( ax^2 + bx + c = 0 \)?
5. Can \( x^2(8 - x) = 0 \) be represented in a graph? If so, what does it look like?

**Tip:** When solving polynomial equations, always check for common factors to simplify the process.

Learn how to solve the equation x^2 * 8 = x^3 with a detailed step-by-step solution. This problem involves algebraic manipulation and factoring of quadratic equations. Suitable for high school students in Grades 10-12.

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