To solve the equation \( 3x^2 = -12 \), we first isolate \( x^2 \) by dividing both sides by 3:
\[ x^2 = \frac{-12}{3} = -4 \]
Next, we observe that \( x^2 = -4 \) has no real solutions, as the square of a real number cannot be negative.
However, we can find complex solutions. We take the square root of both sides:
\[ x = \pm \sqrt{-4} = \pm \sqrt{4} \cdot \sqrt{-1} = \pm 2i \]
Thus, the solutions are:
\[ x = 2i \quad \text{and} \quad x = -2i \]
In total, there are 2 complex solutions to the equation \( 3x^2 = -12 \).