How do you solve $xc^x + x + 1 = 0$ for $x$, where $c$ is a constant?
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There doesn't exist a simple formula, in terms of elementary functions, for finding the roots of functions of this form.
If you need the root for particular $c$ (and $c\neq 0, 1$) you will need to approximate the root, for instance by plotting the function and looking for $x$-intercepts, or asking Wolfram Alpha. There also exist advanced numerical techniques, such as Newton's Method, that you could use to very accurately approximate roots of functions yourself.