To simplify the expression \( 7(2 + 10g^2) + 9g \), we first distribute the \( 7 \) to both terms inside the parentheses:
\[ 7 \times 2 + 7 \times 10g^2 = 14 + 70g^2 \]
Now, we can rewrite the expression:
\[ 14 + 70g^2 + 9g \]
Next, we can arrange the terms in standard form, typically writing the terms in descending order of \( g \):
\[ 70g^2 + 9g + 14 \]
Thus, the simplified expression is:
\[ \boxed{70g^2 + 9g + 14} \]