Step 1: Isolate the cosine term. We are given the equation: $$3\cos(2x) + 9 = -13$$ Subtract 9 from both sides: $$3\cos(2x) = -13 - 9$$ $$3\cos(2x) = -22$$ Divide by 3: $$\cos(2x) = -\frac{22}{3}$$ Step 2: Evaluate the value of $\cos(2x)$. The value $-\frac{22}{3}$ is approximately $-7.33$. Step 3: Check the range of the cosine function. The range of the cosine function is $[-1, 1]$. This means that for any real angle $\theta$, $-1 \le \cos(\theta) \le 1$. Step 4: Determine if a solution exists. Since $-\frac{22}{3}$ is less than $-1$, it falls outside the possible range of values for $\cos(2x)$. Therefore, there is no real angle $2x$ for which $\cos(2x) = -\frac{22}{3}$. Conclusion: There are no solutions for $x$ in the given range $0^\circ \le x < 360^\circ$. $$\boxed{\text{No solution}}$$