To solve for \( x \) in the equation:
\[ -4(3x + 10) - 2 = 54 \]
First, distribute \(-4\) across the terms inside the parentheses:
\[ -4 \cdot 3x - 4 \cdot 10 - 2 = 54 \]
This simplifies to:
\[ -12x - 40 - 2 = 54 \]
Combine the constant terms \(-40\) and \(-2\):
\[ -12x - 42 = 54 \]
Next, isolate the term with \( x \) by adding \( 42 \) to both sides:
\[ -12x - 42 + 42 = 54 + 42 \]
This simplifies to:
\[ -12x = 96 \]
Now, divide both sides by \(-12\):
\[ x = \frac{96}{-12} \]
Calculating the division gives:
\[ x = -8 \]
Thus, the solution is:
\[ \boxed{-8} \]
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