The question explicitly states "A partir de la courbe (C) de la fonction g" (From the curve (C) of the function g). This means we should use the visual information from the graph to determine the solu

The function is $g(x) = -1 + (x-1)\ln x$, defined on $]0, +\infty[$.
We need to find the solutions to the equation $g(x) = 0$.

The question explicitly states "A partir de la courbe (C) de la fonction g" (From the curve (C) of the function g). This means we should use the visual information from the graph to determine the solutions.

The solutions to $g(x) = 0$ are the x-coordinates where the graph of $g(x)$ crosses or touches the x-axis.
Looking at the graph, the curve (C) intersects the x-axis at two distinct points. These points are labeled 'a' and 'b' on the x-axis.

The solutions to the equation $g(x) = 0$ are the values of $x$ indicated by 'a' and 'b' on the graph.

The solutions are $\boxed{\mathbf{x=a \text{ and } x=b}}$.