To solve the equation (x^5 - 2x^4 + x^2 - 2x^2 + x - 2 = 0), we need to simplify the terms and factorize the polynomial as much as possible.

Rearranging the terms, we have:
(x^5 - 2x^4 + (x^2 - 2x^2) + x - 2 = 0).

Combining like terms, we get:
(x^5 - 2x^4 - x^2 + x - 2 = 0).

Now, we can factorize this polynomial by grouping:
(x^2(x^3 - 2x^2) - 1(x^2 - 2) = 0).

Factor out a common factor from the first two terms and the last two terms:
(x^2(x^3 - 2x - 1) - 1(x^2 - 2) = 0).

Factorize further:
(x^2(x^3 - 2x - 1) - 1(x^2 - 2) = 0).

Now, the equation becomes:
(x^2(x - 1)(x^2 + x - 1) - 1(x - 1)(x + 1) = 0).

This can be simplified to:
(x - 1)(x^2(x^2 + x - 1) - 1(x + 1)) = 0).

Thus, the solutions for this equation are:
(x = 1), (x = -1), and solving the quadratic equation (x^2 + x - 1 = 0), we get (x = (-1 ± √5)/2).