  We give a novel description of the recently proposed theory of new massive
gravity (NMG) in three dimensions. We show that in terms of a Dirac type
differential operator acting on the traceless Ricci tensor, the field equations
of the theory reduce to the massive Klein-Gordon type equation with a
curvature-squared source term and to a constraint equation. Under a certain
relation between the source tensor and the traceless Ricci tensor, fulfilled
for constant scalar curvature, the field equations of topologically massive
gravity (TMG) can be thought of as the "square-root" of the massive
Klein-Gordon type equation. Using this fact, we establish a simple framework
for mapping all known algebraic types D and N solutions of TMG into NMG. We
also present new exact solutions of algebraic types D and N which are only
inherent in NMG.
