https://file.aiquickdraw.com/mathbot/file/17270563572276hytuu9v.jpg

The equation in the image is:

\[
v^2 = 18v
\]

To solve for \( v \), we first rearrange the equation:

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

Now factor the equation:

\[
v(v - 18) = 0
\]

This gives us two solutions:

1. \( v = 0 \)
2. \( v - 18 = 0 \) ⟹ \( v = 18 \)

Thus, the solutions are:

\[
v = 0, 18
\]

Would you like more details or have any questions?

Here are five related questions:
1. What happens if the equation was \( v^2 = 20v \)?
2. How do you factor quadratic equations generally?
3. Can you graph the function \( v^2 - 18v = 0 \)?
4. What are the steps for solving equations with more complex factors?
5. How do you solve equations with fractional exponents?

**Tip:** Always try to factor quadratic equations by first checking for common factors before using more complex methods like the quadratic formula.

Learn how to solve the quadratic equation v^2 = 18v by factoring. This algebra problem explores the concepts of factoring and the Zero Product Property. Suitable for students in Grades 7-9.

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