Approaching an Inequality with 4 Variables: Advice & Solution Set

[a4b3c2d1e0f]

Good day, I have this problem that appeared in some practical problem that I'm working on.
I basically want to find the boundaries of a,b,c,d for which the following inequality is satisfied, if a,b,c,d $\in$ ℝ$^+$ and the inequality is:
$-2 \cdot d + c - a \cdot (c \cdot d)^2 + a \cdot c + \frac{1}{a \cdot c \cdot b^2} \ge 0$
How would one approach such a problem, to find the exact solution set?
I'm not really expecting you to solve it, but I'd very much like to hear some advice on how to approach such a problem, to get some information from it, because I want to learn something new.
Thanks

 

[fresh_42]

The inequality relates four variables and maps them to the value of the left hand side. This yields the graph of a function in five dimensional space, a so called four dimensional hypersurface. The solutions are all points on one side of this hypersurface.

I don't see a way to visualize or 'solve' this. One can only make additional assumptions as fixing some variables or perform other projections on lower dimensional spaces.