An algebraically closed groups

Establish the solubility in any algebraically closed group $G$ of each equation of the form
$$ w(x_1, \ldots , x_n)\, = \, g, $$
where $w(x_1, \ldots , x_n)$ — nonempty irreducible group word unknown $x_1,\dots, x_n$, and $g$ — arbitrary element of group $G$.
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