Let's simplify the given equation first:

\[
2x^4 - 4x^2 - 23x - 11x + 6 = 0
\]

Combine the like terms:

\[
2x^4 - 4x^2 - 34x + 6 = 0
\]

Now, the equation is simplified to:

\[
2x^4 - 4x^2 - 34x + 6 = 0
\]

This is a quartic equation, meaning it is a polynomial equation of degree 4. There are several methods for solving such equations, such as factoring (if possible), or using the rational root theorem, numerical methods, or approximations.

Would you like me to continue solving this step-by-step, or would you prefer a particular approach?

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### 5 Related Questions:
1. How do we solve quartic equations in general?
2. What is the Rational Root Theorem and how can it help here?
3. Can this equation be factored directly?
4. How do graphing methods help in solving polynomials?
5. What are synthetic division and its uses in solving polynomials?

#### Tip: For higher-degree polynomials, trying numerical methods or graphing can quickly give you insights into approximate solutions!

Explore the step-by-step solution to the quartic equation 2x⁴ - 4x² - 34x + 6. This problem covers important algebraic concepts such as polynomials and the Rational Root Theorem. Perfect for students in Grades 10-12.

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