To solve the equation \(x^4 + 9 = 12\), we first isolate \(x^4\):
\[ x^4 + 9 = 12 \]
Subtract 9 from both sides:
\[ x^4 = 12 - 9 \]
\[ x^4 = 3 \]
Next, we take the fourth root of both sides:
\[ x = \pm \sqrt[4]{3} \]
Thus, the solutions to the equation are:
\[ x = \sqrt[4]{3} \quad \text{or} \quad x = -\sqrt[4]{3} \]
So the final answer is:
\[ x = \pm \sqrt[4]{3} \]