To solve the first equation, we can rewrite the equation using trigonometric identities.

Given: 3sin^2x - 4sinxcosx + 2cos^2x = 0

Using the identity sin^2x + cos^2x = 1, we can simplify the equation:
3(1 - cos^2x) - 4sinxcosx + 2cos^2x = 0
3 - 3cos^2x - 4sinxcosx + 2cos^2x = 0
-3cos^2x + 2cos^2x - 4sinxcosx + 3 = 0
-cos^2x - 4sinxcosx + 3 = 0

Now, let's analyze the second equation:

Given: sin^2x - 9sinxcosx + 3cos^2x = -1

Using the identity sin^2x + cos^2x = 1, we can simplify the equation:
1 - 9sinxcosx + 3cos^2x = -1
-9sinxcosx + 3cos^2x = -2
-3(3sinxcosx - cos^2x) = -2

These two trigonometric equations can be further manipulated and solved to find the values of x that satisfy the equations.