The equation given is:

\[
6x^2 - 2x = 0
\]

Let's solve for \(x\):

### Step 1: Factor the equation.
We can factor out the common term \(2x\):

\[
2x(3x - 1) = 0
\]

### Step 2: Set each factor equal to 0.
For the product to be zero, one or both of the factors must be zero:

1. \(2x = 0\)
2. \(3x - 1 = 0\)

### Step 3: Solve for \(x\).
For \(2x = 0\):

\[
x = 0
\]

For \(3x - 1 = 0\):

\[
3x = 1 \quad \Rightarrow \quad x = \frac{1}{3}
\]

### Final Answer:
The solutions are:

\[
x = 0 \quad \text{or} \quad x = \frac{1}{3}
\]

Would you like further clarification or additional details?

Here are some related questions you might find interesting:
1. How do you solve quadratic equations using the quadratic formula?
2. What are some methods to factor quadratic equations?
3. How do you find the vertex of a quadratic function?
4. What is the discriminant of a quadratic equation and how does it help?
5. How do you graph quadratic equations?

**Tip:** Always check your solutions by plugging them back into the original equation to ensure they satisfy it!

Learn how to solve the quadratic equation 6x² - 2x = 0 through factoring. This solution covers essential algebra concepts and uses the zero product property. Suitable for students in Grades 8-10.

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