# Calculate: -Variable.H1_{o}sn-

## Expression: $5{k}^{2}-9k+18=4{k}^{2}$

Move the variable to the left-hand side and change its sign

$5{k}^{2}-9k+18-4{k}^{2}=0$

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

$\begin{array} { l }k_1=3,& k_2=6\end{array}$

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