Find all integers satisfying the equation $2^{x} \cdot(4-x)=2 x+4$.
Since $2^{x}$ must be positive, we have $\frac{2 x+4}{4-x}>0$ yielding $-2<x<4$. Thus it suffices to check the points $-1,0,1,2,3$. The three solutions are $x=0,1,2$.