To solve the equation Sin^2x + sinx cosx - 2 cos^2x = 0, we can rewrite it in terms of sine and cosine functions:

sin^2(x) + sin(x)cos(x) - 2cos^2(x) = 0

Let's replace sin(x) with its equivalent in terms of cos(x) using the identity sin^2(x) + cos^2(x) = 1:

cos^2(x) + sin(x)√(1 - cos^2(x)) - 2cos^2(x) = 0

Now, let's simplify the equation:

cos^2(x) + sin(x)√(1 - cos^2(x)) - 2cos^2(x) = 0
cos^2(x) + sin(x)√(1 - cos^2(x)) = 2cos^2(x)
cos^2(x) + sin(x)√(1 - cos^2(x)) = 2cos^2(x)

Solving this equation may still require further simplification or the use of numerical methods.