Variance of a linear combination from a triangular density

The random pair $(X_1,X_2)$ has joint density $f(x_1,x_2)=c\,(1-x_2)$ on the region $0\le x_1\le x_2\le 1$, and zero elsewhere, where $c$ is the constant that makes $f$ integrate to one. Find $\operatorname{Var}(2X_1-4X_2)$.

$11/20$. Normalising gives $c=6$. Then $E[X_1]=\tfrac14$, $E[X_2]=\tfrac12$, $\operatorname{Var}(X_1)=\tfrac{3}{80}$, $\operatorname{Var}(X_2)=\tfrac1{20}$ and $\operatorname{Cov}(X_1,X_2)=\tfrac1{40}$, so the variance is $4\cdot\tfrac3{80}+16\cdot\tfrac1{20}-16\cdot\tfrac1{40}=\tfrac{11}{20}$.