Solve factored polynomial equal to nonzero constant

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I have a polynomial $P(x)$ that is already factored: $P(x) = (x+a_1)(x+a_2)...$. Is there a way to solve $P(x)=c$ where $c \neq 0$ ? Here the $a_i$ are all real. I'm guessing there isn't a general solution, but I'm hoping for a surprise.