x6 - 132x5 +7260x4 - 212960x3 + 3513840x2 - 30921792x + 113379904 = 0. 

The given equation is:

\[
x^6 - 132x^5 + 7260x^4 - 212960x^3 + 3513840x^2 - 30921792x + 113379904 = 0
\]

This is a polynomial equation of degree 6. To solve it, we can attempt several methods, including factoring, synthetic division, or numerical methods like Newton's method. Alternatively, software tools like WolframAlpha or numerical solvers in Python can be used for complex roots.

Let me solve this equation by finding the roots.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can solve this sixth-degree polynomial using numerical methods or symbolic computation tools like WolframAlpha, MATLAB, or a graphing calculator.

Would you like help with an alternative approach or further clarification? Here are five related questions that might interest you:

1. How can we factor high-degree polynomials?
2. What are numerical methods for solving polynomials like this?
3. How does Newton's method work for solving non-linear equations?
4. What are the types of roots a polynomial can have (real, complex, repeated)?
5. How can synthetic division be applied to polynomials?

**Tip**: Always check for rational roots first by using the Rational Root Theorem before diving into more complex methods!

x^6 - 132x^5 + 7260x^4 - 212960x^3 + 3513840x^2 - 30921792x + 113379904 = 0.

Learn how to solve the sixth-degree polynomial equation x^6 - 132x^5 + 7260x^4 - 212960x^3 + 3513840x^2 - 30921792x + 113379904 = 0. This problem covers important algebraic concepts, including polynomial factorization, the Rational Root Theorem, and numerical methods like Newton's method. Suitable for advanced high school or university-level students.

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