  In the 3-3-1 model with right-handed neutrinos, three triplets of scalars
engender the correct sequence of symmetry breaking, $SU(3)_C \times SU(3)_L
\times U(1)_X \rightarrow SU(3)_C \times SU(2)_L \times U(1)_Y \rightarrow
SU(3)_C \times U(1)_{EM}$, generating mass for all fermions, except neutrinos.
Tiny neutrino masses may be achieved by adding one sextet of scalars to the
original scalar content. As consequence, it emerges a very complex scalar
sector, involving terms that violate lepton number explicitly, too. The main
obstacle to the development of the phenomenology of such scenario is the
knowledge of its spectrum of scalars since, now, there are 15 massive scalar
particles on it. The proposal of this work is to do an exhaustive analysis of
such scalar sector with lepton number being explicitly violated at low,
electroweak and high energy scales by means of trilinear terms in the
potential. The first case can be addressed analytically and, as a nice result,
we have observed that the scalar content of such case is split into two
categories: One belonging to the 331 energy scale and the other belonging to
the EWSB energy scale, with the last recovering the well known THDM+triplet.
For the other cases, the scalar sector can be addressed only numerically.
Hence, we proposed a very general approach for the numerical study of the
potential, avoiding simplifications that can make us reach conclusions without
foundation. We show that, in the case of lepton number being explicitly
violated at electroweak scale, it is possible to recover the same physics of
the THDM+triplet, as the previous case. Among all the possibilities, we call
the attention to one special case which generates the 3HDM+triplet scenario.
For the last case, when lepton number is violated at high energy scale, the
sextet become very massive and decouples from the original scalar content of
the 3-3-1 model.
