The expression provided is:

\[
8 + 9y^4 - 6y^3 - 12y
\]

Since this expression is not an equation (it has no equals sign), it cannot be "solved," but it can be simplified, if possible, or factored. Let's analyze it step by step:

1. **Terms**: This is a polynomial with four terms.
   - \(8\) is a constant.
   - \(9y^4\) is a quartic term.
   - \(-6y^3\) is a cubic term.
   - \(-12y\) is a linear term.

2. **Factoring**: The terms do not have a common factor except for the last two terms, which both have a factor of \(y\).
   We can factor out \(-6y\) from the last two terms to get:
   
   \[
   8 + 9y^4 - 6y(y^2 + 2)
   \]

3. **Simplification**: At this point, the expression is as simplified as it can be unless you further manipulate or factor it for specific purposes.

Would you like further steps, such as factoring or evaluating for specific values of \(y\)?

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Here are 5 related questions to explore:
1. How do you factor polynomials of higher degrees?
2. Can this expression be factored completely?
3. What is the degree of the polynomial?
4. How do you determine if a polynomial has real roots?
5. What are the basic steps in simplifying algebraic expressions?

**Tip**: Always check for common factors among terms before factoring further!

This problem covers the simplification and factoring of the polynomial expression 8 + 9y^4 - 6y^3 - 12y. Learn the step-by-step process of identifying terms, factoring common elements, and simplifying algebraic expressions. Suitable for students in Grades 9-12.

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