  For a simply connected (non-nilpotent) solvable Lie group $G$ with a lattice
$\Gamma$ the de Rham and Dolbeault cohomologies of the solvmanifold $G/\Gamma$
are not in general isomorphic to the cohomologies of the Lie algebra $\mathfrak
g$ of $G$. In this paper we construct, up to a finite group, a new Lie algebra
$\tilde{\mathfrak g}$ whose cohomology is isomorphic to the de Rham cohomology
of $G/\Gamma$ by using a modification of $G$ associated with a algebraic
sub-torus of the Zariski-closure of the image of the adjoint representation.
This technique includes the construction due to Guan and developed by the first
two authors. In this paper, we also give a Dolbeault version of such technique
for complex solvmanifolds, i.e. for solvmanifolds endowed with an invariant
complex structure. We construct a finite dimensional cochain complex which
computes the Dolbeault cohomology of a complex solvmanifold $G/\Gamma$ with
holomorphic Mostow bundle and we give a construction of a new Lie algebra
$\breve {\mathfrak g}$ with a complex structure whose cohomology is isomorphic
to the Dolbeault cohomology of $G/\Gamma$.
