Rewrite subtraction as addition of the opposite: $\displaystyle{\left({4}{{z}}^{{2}}\right)}+{10}+{5}{{z}}^{{3}}+{\left(-{2}{{z}}^{{2}}\right)}+{\left(-{15}\right)}\usepackage{cmbright}\Huge\$

Regroup: $\displaystyle{5}{{z}}^{{3}}+{\left({4}{{z}}^{{2}}+-{2}{{z}}^{{2}}\right)}+{\left({10}-{15}\right)}\usepackage{cmbright}\Huge\$

Combine like terms: $\displaystyle{5}{{z}}^{{3}}+{2}{{z}}^{{2}}+{\left(-{5}\right)}={5}{{z}}^{{3}}+{2}{{z}}^{{2}}-{5}\usepackage{cmbright}\Huge\$