To solve the equation \( 20x - 5(6x + 15) = -45 \), we can start by distributing \( -5 \) through the parentheses:
\[ 20x - 5 \cdot 6x - 5 \cdot 15 = -45 \] \[ 20x - 30x - 75 = -45 \]
Next, we combine like terms on the left side:
\[ (20x - 30x) - 75 = -45 \] \[ -10x - 75 = -45 \]
Now, we add \( 75 \) to both sides to isolate the term with \( x \):
\[ -10x - 75 + 75 = -45 + 75 \] \[ -10x = 30 \]
Next, we divide both sides by \( -10 \):
\[ x = \frac{30}{-10} \] \[ x = -3 \]
Thus, the solution to the equation is
\[ \boxed{-3} \]