The optimization of cooperative beamforming vectors in cell-free massive MIMO (mMIMO) systems is presented where multi-antenna access points (APs) support downlink data transmission of multiple users. Albeit the successes of the weighted minimum mean squared error (WMMSE) algorithm and their variants, they lack careful investigations about computational complexity that scales with the number of antennas and APs. We propose a generalized and reduced WMMSE (G-R-WMMSE) approach whose complexity is significantly lower than conventional WMMSE. We partition the set of beamforming coefficients into subvectors, with each subvector corresponding to a specific AP. Such a partitioning approach decomposes the original WMMSE problem across individual APs. By leveraging the Lagrange duality analysis, a closed-form solution can be derived for each subproblem, which substantially reduces the computation burden. Additionally, we present a parallel execution of the proposed G-R-WMMSE with adaptive step sizes, aiming at further reducing the time complexity. Numerical results validate that the proposed G-R-WMMSE schemes achieve over 99% complexity savings compared to the conventional WMMSE scheme while maintaining almost the same performance.