  The quadratic gravity constraints are reformulated in terms of the
Newman-Penrose-like quantities. In such a frame language, the field equations
represent a linear algebraic system for the Ricci tensor components. In
principle, a procedure for the combination of the Ricci components with
standard geometric identities can be applied in a similar way as in the case of
general relativity. These results could serve in various subsequent analyses
and physical interpretations of admitted solutions to quadratic gravity. Here,
we demonstrate the utility of such an approach by explicitly proving general
propositions restricting the spacetime geometry under assumptions on a specific
algebraic type of curvature tensors.
