To simplify the given expression, we can start by applying the double angle formula for sine and cosine:

sin$2x$ = 2sin$x$cos$x$ cos$2x$ = cos^2$x$ - sin^2$x$ = 1 - 2sin^2$x$

Now we can substitute these expressions into the given equation:

2sin$x$cos$x$ + 2$2sin(x)cos(x)$ + 3$1-2si{n}^2(x)$ = 0

Rearranging terms, we get:

2sin$x$cos$x$ + 4sin$x$cos$x$ + 3 - 6sin^2$x$ = 0

Combining like terms:

6sin$x$cos$x$ - 6sin^2$x$ + 3 = 0

Dividing the entire equation by 3:

2sin$x$cos$x$ - 2sin^2$x$ + 1 = 0

Using the double angle formula for sine once again:

2sin$x$cos$x$ - sin^2$x$ + cos^2$x$ = 0

sin^2$x$ + cos^2$x$ = 1

Therefore, the simplified expression is:

1 = 1

So, the given equation simplifies to 1 = 1, which is always true.