To simplify this trigonometric equation, we can use the double angle formula for sine:

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

Let's rewrite the equation using the double angle formula:

5sin(3/2π - x) + 2(2sin(π - x)cos(π - x)) - 2 = 0
5sin(3/2π - x) + 4sin(π - x)cos(π - x) - 2 = 0

Now, we know that sin(π - x) = sin(x) and cos(π - x) = -cos(x). So we can further simplify:

5sin(3/2π - x) + 4sin(x)(-cos(x)) - 2 = 0
5sin(3/2π - x) - 4sin(x)cos(x) - 2 = 0

Now let's use the double angle formula for sine once again:

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

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

Substitute this back into the equation:

5sin(3/2π - x) - 2sin(2x) - 2 = 0

So the simplified form of the trigonometric equation is:

5sin(3/2π - x) - 2sin(2x) - 2 = 0