To solve the equation 2sin(3x) = -1, we first isolate sin(3x) by dividing both sides by 2:

sin(3x) = -1/2

Now we need to find the solutions for sin(3x) = -1/2. The sine function has a value of -1/2 at two different angles: -30 degrees and -150 degrees. These angles correspond to the solutions for 3x when x is in the range of 0 to 2π.

So, we have:

3x = -30 degrees, -150 degrees

Now we solve for x by dividing both sides by 3:

x = -10 degrees, -50 degrees

Therefore, the solutions for the equation 2sin(3x) = -1 are x = -10 degrees and x = -50 degrees.