https://file.aiquickdraw.com/mathbot/file/1728315042077fhtfg3nx.jpg

The given equation is:

\[
6v^2 - 18v = 0
\]

Let's solve it step by step:

1. Factor the equation:
\[
6v(v - 3) = 0
\]

2. Set each factor equal to zero:
\[
6v = 0 \quad \text{or} \quad v - 3 = 0
\]

3. Solve each equation:
\[
v = 0 \quad \text{or} \quad v = 3
\]

Thus, the solutions for \(v\) are:

\[
v = 0, 3
\]

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How do you factor a quadratic equation in general?
2. What are the methods to solve quadratic equations other than factoring?
3. Why does factoring work to find solutions of quadratic equations?
4. Can a quadratic equation have more than two solutions?
5. How can you solve a quadratic equation that doesn't factor easily?

**Tip:** Always check if you can factor out a common term in quadratic equations. It simplifies solving.

Learn how to solve the quadratic equation 6v^2 - 18v = 0 using factoring. This problem highlights key algebraic concepts such as factoring and the zero product property. Suitable for students in Grades 7-9.

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