Let's solve the equation \( 420 = 25r + 15 \cdot 3r \).
First, simplify the term \( 15 \cdot 3r \):
\[ 15 \cdot 3r = 45r \]
Now, substitute this back into the equation:
\[ 420 = 25r + 45r \]
Combine the like terms \( 25r \) and \( 45r \):
\[ 420 = 70r \]
Now, to isolate \( r \), divide both sides by 70:
\[ r = \frac{420}{70} \]
Calculating the right side:
\[ r = 6 \]
So, the value of \( r \) is \( \boxed{6} \).