Let's simplify the given equation step by step.

-3(1 + 4x) = -4x - 5
-3 1 + (-3 4x) = -4x - 5
-3 - 12x = -4x - 5

Now, let's isolate the variable x by combining like terms:

-12x = -4x - 5 + 3
-12x = -4x - 2

Now, let's move all the x terms to one side of the equation:

-12x + 4x = -2
-8x = -2

Lastly, divide by -8 to solve for x:

x = -2 / -8
x = 1/4

Therefore, the solution to the equation -3(1 + 4x) = -4x - 5 is x = 1/4.