2x^4+1>=2x^3+x^2

2x^4+1 ≥ 2x^3+x^2     subtract 2x^3+x^2 from both sides

2x^4 - 2x^3 - x^2 + 1 ≥ 0      this is probably most easily solved by graphing

Here's the graph.......https://www.desmos.com/calculator/qgn7o2v8vm

Note that this graph is ≥ 0  for all x values......so....the solution to this is  (-∞, ∞ )