Answer
$x=a^{2} -3a+2$
Work Step by Step
Subtract $6$ from both sides and factor x out on the LHS.
$ x(a-3)=a^{3}-6a^{2}+11a-6\quad$... divide with $(a+2)$
$ x=\displaystyle \frac{a^{3}-6a^{2}+11a-6}{a-3}\quad$... perform long division
$ \begin{array}{llllllll}
& & a^{2} & -3a & +2 & & & \color{red}{ \small{Quotient}} \\
& & -- & -- & -- & -- & & \\
a-3 & ) & a^{3} & -6a^{2} & +11a & -6 & & \\
& & a^{3} & -3a^{2} & & & & \color{red}{\leftarrow \small{ a^{2}(a-3) } } \\
& & -- & -- & & & & \color{red}{\leftarrow \small{ subtract } } \\
& & & -3a^{2} & +11a & -6 & & \\
& & & -3a^{2} & +9a & & & \color{red}{\leftarrow \small{-3a(a-3) } }\\
& & & -- & -- & & & \color{red}{\leftarrow \small{ subtract }} \\
& & & & 2a & -6 & & \\
& & & & 2a & -6 & & \color{red}{\leftarrow \small{2(a-3) } }\\
& & & & -- & -- & & \color{red}{\leftarrow \small{ subtract }} \\
& & & & & 0 & & \color{red}{\leftarrow \small{ Remainder } }
\end{array}$
$x=a^{2} -3a+2$
