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To solve the equation \(-5(3x - 3) + 4x - 5 = -12\), we will first simplify the left-hand side.
1. Distribute \(-5\) across \((3x - 3)\):
\[
-5(3x) + (-5)(-3) = -15x + 15
\]
So the equation becomes:
\[
-15x + 15 + 4x - 5 = -12
\]
2. Combine like terms:
\[
-15x + 4x + 15 - 5 = -12
\]
This simplifies to:
\[
-11x + 10 = -12
\]
3. Next, isolate the term with \(x\) by subtracting 10 from both sides:
\[
-11x = -12 - 10
\]
Thus,
\[
-11x = -22
\]
4. Now, divide both sides by \(-11\):
\[
x = \frac{-22}{-11} = 2
\]
So, the solution to the equation is:
\[
\boxed{2}
\]