2x^4-2x^3-11x^2-x-6=0

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To solve this equation, we can use factoring by grouping.

First, let's rewrite the equation as follows:

2x^4 - 2x^3 - 11x^2 - x - 6 = 0

Now, let's group the terms:

(2x^4 - 2x^3) - (11x^2 + x) - 6 = 0

Factor out common terms from each group:

2x^3(x - 1) - x(11x + 1) - 6 = 0

Now, we can factor out a common factor from the terms inside the parentheses:

2x^3(x - 1) - x(11x + 1) - 6 = 0

(2x^3 - x)(x - 1) - 6 = 0

Now, we can factor further:

x(2x^2 - 1)(x - 1) - 6 = 0

x(√2x + 1)(√2x - 1)(x - 1) - 6 = 0

Now, we have factored the equation completely. The solutions to the equation are x = 1, x = -1/√2, x = 1/√2.