To factor the expression \( 36a^2 + 24a \) completely, we can first look for the greatest common factor (GCF) of the terms.
The GCF of the coefficients 36 and 24 is 12, and both terms contain the variable \( a \). Therefore, the GCF is \( 12a \).
Now we can factor out \( 12a \) from the expression:
\[ 36a^2 + 24a = 12a(3a) + 12a(2) = 12a(3a + 2) \]
Thus, the completely factored form of the expression is:
\[ \boxed{12a(3a + 2)} \]