To solve the equation \(8x^2 - 4x = 0\), you can follow these steps:

1. **Factor out the common term:**
\[
8x^2 - 4x = 0
\]
Both terms on the left-hand side have a common factor of \(4x\). So, factor \(4x\) out:
\[
4x(2x - 1) = 0
\]

2. **Set each factor equal to zero:**
For the product to be zero, at least one of the factors must be zero. Therefore, set each factor equal to zero:
\[
4x = 0 \quad \text{or} \quad 2x - 1 = 0
\]

3. **Solve each equation:**

- For \(4x = 0\):
\[
x = 0
\]

- For \(2x - 1 = 0\):
\[
2x = 1
\]
\[
x = \frac{1}{2}
\]

So, the solutions to the equation \(8x^2 - 4x = 0\) are:
\[
x = 0 \quad \text{or} \quad x = \frac{1}{2}
\]