To solve the equation \((x−3)^2−81=0\), we can start by rewriting it:
\[ (x - 3)^2 = 81 \]
Next, we take the square root of both sides, keeping in mind that there will be both positive and negative square roots:
\[ x - 3 = 9 \quad \text{or} \quad x - 3 = -9 \]
Now, we solve each equation separately:
- For \(x - 3 = 9\):
\[ x = 9 + 3 = 12 \]
- For \(x - 3 = -9\):
\[ x = -9 + 3 = -6 \]
Thus, the solutions to the equation are:
\[ x = 12 \quad \text{and} \quad x = -6 \]
From the provided options, the only solution given is:
12
Therefore, the correct answer is 12.