Answer
$10z^2-16z$
Work Step by Step
Removing the grouping symbols and then combining like terms, the given expression, $
-[3z^2+5z-(2z^2-6z)]+[(8z^2-[5z-z^2])+2z^2]
,$ simplifies to
\begin{array}{l}\require{cancel}
-[3z^2+5z-2z^2+6z]+[(8z^2-5z+z^2)+2z^2]
\\\\=
-[3z^2+5z-2z^2+6z]+[8z^2-5z+z^2+2z^2]
\\\\=
-3z^2-5z+2z^2-6z+8z^2-5z+z^2+2z^2
\\\\=
(-3z^2+2z^2+8z^2+z^2+2z^2)+(-5z-6z-5z)
\\\\=
10z^2-16z
.\end{array}