While I was studying my maths book, I came across this equation:
$$ xe^{-x}+2e^{-x}=0 $$
I tried to solve it in different ways, but each time I break up some rule. My best try was this:
Let's $u=e^{-x}$, thus we have: $$ xu+2u=0 $$ By taking $u$ as a common factor we get:
$$ u(x+2)=0 $$
By dividing both side by $(x+2)$ we get:
$$ u=0 $$
But $u=e^{-x}$, then:
$$ e^{-x}=0 \\ ln(e^{-x}) = ln(0) ?? $$
$ln(0)$ is obviously wrong, where did I slip?