problem: What is the value of $x$ in the equation $6^{x+1}-6^{x}=1080$?
solution: Rewrite the left-hand side as $6^x(6^1-6^0)=6^x\cdot5$.  Divide both sides by $5$ to find $6^x=\frac{1080}{5}=216$.  Since $216=6^3$, $x=\boxed{3}$.