  A new proposed one dimensional time independent Schr\"odinger equation is
solved completely using shape invariance method. The corresponding potential is
given by V_(x,A,B) =-A(sechpx)^2 - 6Bp(sech6px)^2+(tanhpx-6tanh6px)^2 with
superpotential W(x,A,B) = Atanh(px)+Btanh(6px). We derive the exact solutions
of the family of Schr\"odinger equations with the V_- potential partner using
supersymmetric quantum mechanics technique of a superpotential having shape
invariance property, and where the discrete spectrum and the corresponding
eigenfunctions are determined exactly and in closed form. It is well-known that
Schr\"odinger equations are challenging to solve in closed form, and only a few
of them are known. Finding new equations with exact solutions is crucial in
understanding the hidden physical properties near turning points where
numerical methods fail in these vicinities. This result has potential
applications in nuclear physics and chemistry where the antagonist forces have
a prominent presence.
