Consider the following sum: $\displaystyle{\left(-{4}{{a}}^{{2}}+{3}{a}-{2}\right)}+{\left({k}{{a}}^{{2}}+{2}\right)}={3}{a}\usepackage{cmbright}\Huge\$ . Determine the value of $\displaystyle{k}\usepackage{cmbright}\Huge\$ that will make the equation true.