Based on my previous two questions (that failed), I am trying once more.
What are some simplified conditions for which:
$$W\bigg(A-\frac{X}{W}\bigg)^3\bigg[X-AW-\frac{AY}{N}(B+D)-\frac{AZ}{N}(C+D+E+F+G)\bigg]+\frac{X}{N}\bigg[Y(A+H)(B+D)+AZ(C+D+E+F+G)\bigg]<0$$
WHERE:
All of the letters are positive parameters (not constants) and:
$1.$ $$A,B,C,D,E,F,G,H < N \implies \frac{A}{N},\frac{B}{N},\frac{C}{N},\frac{D}{N},\frac{E}{N},\frac{F}{N},\frac{G}{N},\frac{H}{N} <1 $$
$2.$ $AW>X$
Is this problem tractable by hand, or do I have to use Maple/Matlab to simplify my expression somehow?
Well, $C$, $E$, $F$, and $G$ only ever appear in the combination $C+E+F+G$, so the first manual reduction is $C+E+F+G \rightarrow C'$, eliminating ~$1/3$ of the parameters. Multiply through by $N W^2$ to eliminate denominators. The second summand is entirely positive, so collapse it to, say, $V$ (now $H$ is gone too). Having Mathematica (9.0) attack the resulting expression (and ignoring the implicit relationship between $V$ and $A,B,C',D,H,W,X,Y,\text{ and }Z$): $$V-(A W-X)^3 (A (Y (B+d)+Z (C'+D)+N W)-N X)<0$$ yields a solution set composed of 96 parts. (We're lucky. It's not so hard to construct something about as complicated with over 1000 distinct solution components.) An easy one: $$0<A, 0<B<A/4, 4A \leq C', C'/4 < D, D < N, 0 < V, \{\zeta \in \mathbb{R}_{>0} \mid A^4 N \zeta^4 - V = 0\}_2 < W, \\ 0 < X \leq \{ \zeta \in \mathbb{R}_{>0} \mid \zeta^4-4AW\zeta^3+6A^2W^2\zeta^2-4A^3W^3\zeta+A^4W^4 -V/N = 0\}_1, 0 < Y, \text{ and } 0 < Z$$ where I've used the nonstandard notation $\{\text{variable} \mid \text{polynomial}=0\}_n$ to mean the $n^\text{th}$ element in the ordered list of roots of the polynomial, in a specific (complicated to describe) order. Every component has at least one of these polynomial roots in it. (Scanning suggests two or three of these root-findings per component, in general.)
Enforcing the implicit relationship between $V$ and $A,B,C',D,H,W,X,Y,\text{ and }Z$ and also the relationship between $C'$ and $C,E,F, \text{ and } H$ won't improve the situation at all.
What kind of conditions were you hoping for?