https://file.aiquickdraw.com/mathbot/file/172705663945304x7qw38.jpg

The equation in the image appears to be:

\[
3x^2 + 3y^2 + 6y = 0
\]

This is a quadratic equation involving both \(x\) and \(y\). To solve or simplify it, let's start by working with the terms.

Would you like me to solve for \(y\) in terms of \(x\), or simplify this equation further? Let me know how you'd like to proceed!

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Here are five follow-up questions to expand on this:

1. What are the typical steps to solve a quadratic equation involving two variables like this one?
2. Can this equation be factored, and if so, how would that affect the solution?
3. What would be the geometric interpretation of this equation?
4. How would adding or changing coefficients affect the general shape or solution?
5. How can we test if this equation has real solutions?

**Tip:** In many quadratic equations involving two variables, completing the square is a useful method for simplification.

Solve the quadratic equation 3x^2 + 3y^2 + 6y = 0.

Learn how to solve the multivariable quadratic equation 3x^2 + 3y^2 + 6y = 0. The solution involves simplifying and factoring, and interpreting the geometric representation of this equation. Ideal for students in Grades 9-12.

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