The extraction of aluminum metal from the aluminum hydroxide in bauxite ore by the Hall$-$H$$roult process is one of the most remarkable success stories of late

$19$th century practical chemistry, turning aluminum from a rare and precious metal into the cheap commodity it is today. In the first step, aluminum hydroxide

reacts to form alumina and water:

$2Al(OH{)}_3(s)A{l}_2{O}_3(s)+3H_{2}O(g)$

In the second step, alumina and carbon react to form aluminum and carbon dioxide:

$2A{l}_2{O}_3(s)+3C(s)4Al(s)+3C{O}_2(g)$

Write the net chemical equation for the production of aluminum from aluminum hydroxide and carbon. Be sure your equation is balanced.