Condition: $x\geq -1$
Disequations $\Leftrightarrow 4(\sqrt{x+1}-2)+2(\sqrt{2x-3})\leq x^3-x^2-2x-12$
$\Leftrightarrow \frac{4(x-3)}{2+\sqrt{x+1}}+\frac{4(x-3)}{3+\sqrt{2x+3}}-(x-3)(x^2+2x+4)\leq 0$
$(x-3)$$[\frac{4}{2+\sqrt{x+1}}+\frac{4}{3+\sqrt{2x+3}}-(x+1)^2-3]$$\leq 0$
$+)x=-1$ is satisfy.
$+)x>-1\rightarrow $ Blue $<\frac{4}{2+0}+\frac{4}{3+1}-0-3=0$
$\rightarrow ...............$
$\rightarrow x\geq 3.$
Combined with condition, we get:
$x=-1$ v $x\geq 3$