First, let's simplify the terms within the parentheses.

2(x² + 1/x²) = 2x² + 2/x²

-11(x - 1/x) = -11x + 11/x

Now let's rewrite the equation:

2x² + 2/x² - 11x + 11/x + 8 = 0

Now let's find a common denominator to combine the terms:

(2x^4 + 2 - 11x^3 + 11x^2 + 8x^2)/x^2 = 0

Combine the like terms:

2x^4 - 11x^3 + 19x^2 + 2 = 0

This is the simplified form of the given equation.