To factor the expression \( 54 + 45x \) completely, we first look for the greatest common factor (GCF) of the coefficients 54 and 45.
The factors of each number are:
- Factors of 54: \( 1, 2, 3, 6, 9, 18, 27, 54 \)
- Factors of 45: \( 1, 3, 5, 9, 15, 45 \)
The greatest common factor of 54 and 45 is 9.
Now, we can factor out 9 from the expression:
\[ 54 + 45x = 9(6 + 5x) \]
Thus, the completely factored form of the expression is:
\[ \boxed{9(6 + 5x)} \]