To solve this equation, we need to expand the left side and then set it equal to 0:

(sin2x - 1)(cos3x - 1/2) = -0

Expand the left side using the distributive property:

sin(2x)cos(3x) - sin(2x)(1/2) - cos(3x) + 1/2 = 0

Now, we need to simplify the expression by using trigonometric identities and then solve for x:

(sin(2x)cos(3x) = sin(2x)cos(3x) using product-to-sum identities

Next, we substitute the identity above into the expanded equation:

sin(2x)cos(3x) - (1/2)sin(2x) - cos(3x) + 1/2 = 0

Now, we have the equation in terms of sin and cos functions. We can solve for x by trying to isolate the trigonometric functions and solving the resulting equation.
Further simplifications are needed to find the exact solution.