To solve the equation 15 - 2(x - 1) = -3, we can follow these steps:

1. Distribute the -2 to the terms inside the parentheses:
15 - 2(x) + 2(1) = -3

2. Simplify the equation:
15 - 2x + 2 = -3

3. Combine like terms:
17 - 2x = -3

4. Move the constant term to the other side of the equation by adding 3 to both sides:
17 - 2x + 3 = -3 + 3
20 - 2x = 0

5. Move the variable term to the other side of the equation by subtracting 20 from both sides:
20 - 2x - 20 = 0 - 20
-2x = -20

6. Divide both sides of the equation by -2 to solve for x:
(-2x) / -2 = (-20) / -2
x = 10

Therefore, the solution to the equation 15 - 2(x - 1) = -3 is x = 10.