Massive multi-user (MU) MIMO wireless technology promises improved spectral efficiency compared to that of traditional cellular systems. While data-detection algorithms that rely on linear equalization achieve near-optimal error-rate performance for massive MU-MIMO systems, they require the solution to large linear systems at high throughput and low latency, which results in excessively high receiver complexity. In this paper, we investigate a variety of exact and approximate equalization schemes that solve the system of linear equations either explicitly (requiring the computation of a matrix inverse) or implicitly (by directly computing the solution vector). We analyze the associated performance/complexity trade-offs, and we show that for small base-station (BS)-to-user-antenna ratios, exact and implicit data detection using the Cholesky decomposition achieves near-optimal performance at low complexity. In contrast, implicit data detection using approximate equalization methods results in the best trade-off for large BS-to-user-antenna ratios. By combining the advantages of exact, approximate, implicit, and explicit matrix inversion, we develop a new frequency-adaptive e qualizer (FADE), which outperforms existing data-detection methods in terms of performance and complexity for wideband massive MU-MIMO systems.