  Using the BPS Lagrangian method, we show that gravity theory coupled to
matter in various dimensions may possess Bogomol'nyi-like equations, which are
first-order differential equations, satisfying the Einstein equations and the
Euler-Lagrange equations of classical fields ($U(1)$ gauge and scalar fields).
In particular we consider static and spherically symmetric solutions by taking
proper ansatzes and then we find an effective Lagrangian density that can
reproduce the Einstein equations and the Euler-Lagrange equations of the
classical fields. We consider the BPS Lagrangian density to be linear function
of first-order derivative of all the fields. From these two Lagrangian desities
we are able to obtain the Bogomol'nyi-like equations whose some of solutions
are well-known such as Schwarzschild, Reissner-Nordstr\"{o}m, Tangherlini black
holes, and the recent black holes with scalar hair in three dimensions [Phys.
Rev. D 107, 124047]. Using these Bogomol'nyi-like equations, we are also able
to find new solutions for scalar hair black holes in three and four dimensional
spacetime. Furthermore we show that the BPS Lagrangian method can provide a
simple alternative proof of black holes uniqueness theorems in any dimension.
