$5{k}^{2}-9k+18-4{k}^{2}=0$
Collect like terms${k}^{2}-9k+18=0$
Write $-9k$ as a difference${k}^{2}-3k-6k+18=0$
Factor out $k$ from the expression$k \times \left( k-3 \right)-6k+18=0$
Factor out $-6$ from the expression$k \times \left( k-3 \right)-6\left( k-3 \right)=0$
Factor out $k-3$ from the expression$\left( k-3 \right) \times \left( k-6 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }k-3=0,\\k-6=0\end{array}$
Solve the equation for $k$$\begin{array} { l }k=3,\\k-6=0\end{array}$
Solve the equation for $k$$\begin{array} { l }k=3,\\k=6\end{array}$
The equation has $2$ solutions$\begin{array} { l }k_1=3,& k_2=6\end{array}$