First, distribute the -4 and -3 on the left side, and -3 on the right side:

-4x - 4 - 3 = -3x + 12

Combine like terms:

-4x - 7 = -3x + 12

Next, move all the terms involving x to one side of the equation:

-4x + 3x = 12 + 7

Simplify:

-x = 19

Multiply both sides of the equation by -1 to solve for x:

x = -19

Therefore, the solution to the equation -4(x + 1) - 3 = -3(x - 4) is x = -19.