To solve the equation \(-4(4x - 5) = 4x\), let's begin by distributing \(-4\) on the left side:
\[ -4(4x - 5) = -4 \cdot 4x + (-4) \cdot (-5) = -16x + 20 \]
So, the equation becomes:
\[ -16x + 20 = 4x \]
Next, we can move all terms involving \(x\) to one side of the equation. To do this, add \(16x\) to both sides:
\[ 20 = 4x + 16x \]
This simplifies to:
\[ 20 = 20x \]
Now, divide both sides by 20:
\[ x = 1 \]
Thus, the solution to the equation is:
\[ \boxed{1} \]