Step 1 :Given expression is \(54 + 45x\).
Step 2 :Find the greatest common factor (GCF) of the terms 54 and 45, which is 9.
Step 3 :Factor out the GCF from the expression: \(54 + 45x = 9(6 + 5x)\).
Step 4 :\(\boxed{9(6 + 5x)}\) is the completely factored form of the expression \(54 + 45x\).