To solve for \( x \) in the equation
\[ -4(3x + 10) = 56, \]
first, we'll distribute the \(-4\) on the left side:
\[ -4 \cdot 3x - 4 \cdot 10 = 56 \]
which simplifies to
\[ -12x - 40 = 56. \]
Next, we can add \( 40 \) to both sides of the equation:
\[ -12x - 40 + 40 = 56 + 40, \]
which simplifies to
\[ -12x = 96. \]
Now, we will divide both sides by \(-12\):
\[ x = \frac{96}{-12}, \]
which simplifies to
\[ x = -8. \]
Thus, the solution for \( x \) is
\[ \boxed{-8}. \]