To solve this equation for x, we can rewrite it in terms of a single trigonometric function.

First, we can rewrite the equation as:

3 sinx + 2 cosx = 3
3 sinx = 3 - 2 cosx
sinx = (3 - 2 cosx) / 3

Next, we can use the trigonometric identity, sin^2x + cos^2x = 1, to rewrite sinx in terms of cosx:

sin^2x = 1 - cos^2x
sinx = ±√(1 - cos^2x)

Substitute sinx = ±√(1 - cos^2x) into the equation sinx = (3 - 2 cosx) / 3:

±√(1 - cos^2x) = (3 - 2 cosx) / 3
±(1 - cos^2x) = (3 - 2 cosx)^2 / 9
±(1 - cos^2x) = (9 - 12cosx + 4cos^2x) / 9
±9 - 9 cos^2x = 9 - 12cosx + 4cos^2x
9 cos^2x - 4cosx - 8 = 0

Now, we have a quadratic equation in terms of cosx. We can solve this quadratic equation to find the possible values of cosx, and then use these values to find the corresponding values of x.