To solve the equation \(-6.29 ( x + 7.85 ) = -19.499\), we can start by dividing both sides by \(-6.29\):
\[ x + 7.85 = \frac{-19.499}{-6.29} \]
Calculating the right side:
\[ \frac{-19.499}{-6.29} = \frac{19.499}{6.29} \approx 3.1 \]
So we have:
\[ x + 7.85 \approx 3.1 \]
Next, we isolate \(x\) by subtracting \(7.85\) from both sides:
\[ x \approx 3.1 - 7.85 \]
Calculating that gives:
\[ x \approx -4.75 \]
Hence, the solution is:
\[ \boxed{-4.75} \]