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

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

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

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

Now, let's move all terms to one side of the equation:

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

This is a polynomial equation of degree 4. To solve it, we can try factoring, but it doesn't seem to be factorable. Another option is to use numerical methods or a graphing calculator to find the approximate solutions.