To solve this equation, we can combine like terms and simplify:

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

Expanding the terms inside the parentheses:

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

Combining like terms:

-x^2 + 2x - 3 = 0

To solve for x, we can set this equation equal to zero and factor:

-x^2 + 2x - 3 = 0

Factor out a negative from the left side:

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

Now we need to factor the quadratic inside the parentheses:

x^2 - 2x + 3 cannot be factored using real numbers, so we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -2, and c = 3:

x = (2 ± sqrt((-2)^2 - 413)) / 2*1
x = (2 ± sqrt(4 - 12)) / 2
x = (2 ± sqrt(-8)) / 2

Since the square root of -8 is not a real number, the equation has no real solutions.