To solve the equation sin(6x) * cos(6x) = -1/2, we can use the double angle formula for sine:

sin(2θ) = 2sin(θ)cos(θ)

Plugging in θ = 6x, we get:

sin(12x) = 2sin(6x)cos(6x)

Now we can rewrite the given equation using this double angle formula:

2sin(6x)cos(6x) = -1/2

Since sin(12x) = 2sin(6x)cos(6x), we can substitute sin(12x) into the equation:

sin(12x) = -1/2

To find the solutions for this equation, we need to determine where the sine function equals -1/2. This occurs at 30 degrees or pi/6 in radians.

Therefore, the solutions for x are:

12x = π/6 + 2nπ or 12x = 5π/6 + 2nπ, where n is an integer.

Solving for x, we get:

x = π/72 + nπ/6 or x = 5π/72 + nπ/6, where n is an integer.