We consider type I+II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos m_ν and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix f, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any

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... f, there is a dual solution f̂=m_ν/v_L-f, where v_L is the VEV of the triplet Higgs. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix f. For n lepton generations the number of solutions is 2^n. We develop an exact analytic method of solving the seesaw non-linear matrix equation for f.