To solve the equation 2cos^2(x) - cos(x) - 1 = 0, we can use factoring or the quadratic formula.

Using factoring:
Let's rewrite the equation as 2cos^2(x) - 2cos(x) + cos(x) - 1 = 0.
Group the terms: (2cos^2(x) - 2cos(x)) + (cos(x) - 1) = 0.
Factor out common terms: 2cos(x)(cos(x) - 1) + 1(cos(x) - 1) = 0.
Factor out (cos(x) - 1): (2cos(x) + 1)(cos(x) - 1) = 0.

Now, set each factor equal to zero:
2cos(x) + 1 = 0 or cos(x) - 1 = 0.

For 2cos(x) + 1 = 0:
2cos(x) = -1.
cos(x) = -1/2.
x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.

For cos(x) - 1 = 0:
cos(x) = 1.
x = 2πn, where n is an integer.

Therefore, the solutions to the equation 2cos^2(x) - cos(x) - 1 = 0 are x = π/3 + 2πn, x = 5π/3 + 2πn, and x = 2πn, where n is an integer.