To simplify the given equation, we can use trigonometric identities to simplify each term.

Starting with the first term 3cos(2x), we can use the double angle identity for cosine:

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

Substitute this into the first term:

3cos(2x) = 3(cos^2(x) - sin^2(x))

= 3cos^2(x) - 3sin^2(x)

Moving on to the second term 3sin(x) * cos(x), we can use the product-to-sum identity:

sin(a)cos(b) = 0.5[cos(a-b) - cos(a+b)]

Substitute x for a in this case:

3sin(x)cos(x) = 1.5[cos(0) - cos(2x)]

= 1.5(1 - cos(2x))

Lastly, for the third term -2sin(2x), we can again use the double angle identity for sine:

sin(2x) = 2sin(x)cos(x)

Substitute this into the third term:

-2sin(2x) = -4sin(x)cos(x)

Now replace each term in the original equation with their simplified forms:

3cos^2(x) - 3sin^2(x) + 1.5(1 - cos(2x)) - 4sin(x)cos(x) = 2

Simplify the equation further by combining like terms and solving for x.