Let's simplify and solve the equation step by step.

The equation given is:

\[ 15 - 3.13(x - 1) - (-2) = -10 \]

First, let's simplify the left side of the equation. Notice that \(-(-2)\) is equivalent to \(+2\):

\[
15 - 3.13(x - 1) + 2 = -10
\]

Combine the constant terms on the left:

\[
17 - 3.13(x - 1) = -10
\]

Next, isolate the term with \(x\) by subtracting 17 from both sides:

\[
-3.13(x - 1) = -10 - 17
\]
\[
-3.13(x - 1) = -27
\]

Now, divide both sides by \(-3.13\):

\[
x - 1 = \frac{-27}{-3.13}
\]

Calculating the right side:

\[
x - 1 \approx 8.619
\]

Now, add 1 to both sides to solve for \(x\):

\[
x \approx 8.619 + 1
\]
\[
x \approx 9.619
\]

So the solution for \(x\) is approximately:

\[
x \approx 9.62
\]

Thus, the answer is:

\[
x \approx 9.62
\]