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The given quadratic equation is:

\[
4x^2 = 32x
\]

To solve by factoring, follow these steps:

### Step 1: Rearrange the equation
Move all terms to one side of the equation:

\[
4x^2 - 32x = 0
\]

### Step 2: Factor out the greatest common factor (GCF)
The GCF of \(4x^2\) and \(-32x\) is \(4x\), so factor that out:

\[
4x(x - 8) = 0
\]

### Step 3: Solve for \(x\)
Now that the equation is factored, use the zero product property, which states that if \(a \cdot b = 0\), then either \(a = 0\) or \(b = 0\).

- Set \(4x = 0\), which gives \(x = 0\).
- Set \(x - 8 = 0\), which gives \(x = 8\).

### Final Solution:
The factored form is:

\[
4x(x - 8) = 0
\]

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

Would you like further details or clarification? Here are some related questions:

1. What is the zero product property and how does it work?
2. How do you determine the greatest common factor when factoring?
3. What are some alternative methods for solving quadratic equations?
4. Can all quadratic equations be factored?
5. How do you check if the factored solution is correct?

**Tip:** Always check your solutions by plugging them back into the original equation to verify that they satisfy the equation.

Solve the quadratic equation 4x^2 = 32x by factoring.

Learn how to solve the quadratic equation 4x^2 = 32x by factoring. This solution includes finding the greatest common factor (GCF), applying the zero product property, and solving for x. Suitable for students in Grades 8-10.

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