https://file.aiquickdraw.com/mathbot/file/17255903273148vyziuq7.jpg

The text extracted from the image seems unclear. Based on the visual analysis of the equation in the image, it appears to be:

\[
6(2y + 5)(1 - y) = -2y - 6
\]

I'll now solve this equation.

### Steps to solve:

1. Expand both sides of the equation.
2. Simplify and collect like terms.
3. Solve for \( y \).

Let me proceed with the calculations.The solutions to the equation \( 6(2y + 5)(1 - y) = -2y - 6 \) are:

\[
y = \frac{-2 + \sqrt{31}}{3} \quad \text{or} \quad y = \frac{-2 - \sqrt{31}}{3}
\]

These are the exact solutions in simplified radical form.

Would you like further details or explanations about this solution? Here are a few related questions to expand your understanding:

1. How can we verify the solution of a quadratic equation?
2. What is the process of expanding and simplifying algebraic expressions?
3. How do you interpret the square root in a real-world context?
4. Can this equation have any real-life applications, and if so, what are they?
5. What does it mean when an equation has two distinct solutions?

**Tip:** Always check for extraneous solutions when solving complex equations, especially if squaring both sides at some point.

This problem demonstrates how to solve a quadratic equation in algebra by expanding and simplifying the terms. The solution involves using the quadratic formula. Suitable for Grades 9-10 students.

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