To solve the equation \(-3(-4x - 3) = -27\), we first distribute the \(-3\) on the left side:
\[ -3(-4x) - 3(-3) = 12x + 9 \]
So the equation becomes:
\[ 12x + 9 = -27 \]
Next, we isolate \(12x\) by subtracting \(9\) from both sides:
\[ 12x = -27 - 9 \] \[ 12x = -36 \]
Now we divide both sides by \(12\):
\[ x = \frac{-36}{12} \] \[ x = -3 \]
Thus, the solution is:
\[ \boxed{-3} \]