Answer
The solution of the equation is $\left\{ \underline{-3,2,\frac{1}{2}} \right\}$
Work Step by Step
We consider the provided equation:
$2{{x}^{3}}+{{x}^{2}}-13x+6=0$
Factorize and solve the equation as given below:
$\begin{align}
& 2{{x}^{3}}-4{{x}^{2}}+5{{x}^{2}}-10x-3x+6=0 \\
& 2{{x}^{2}}\left( x-2 \right)+5x\left( x-2 \right)-3\left( x-2 \right)=0 \\
& \left( x-2 \right)\left( 2{{x}^{2}}+5x-3 \right)=0 \\
& \left( x-2 \right)\left( 2{{x}^{2}}+6x-x-3 \right)=0
\end{align}$
$\begin{align}
& \left( x-2 \right)\left( 2x\left( x+3 \right)-1\left( x+3 \right) \right)=0 \\
& \left( x-2 \right)\left( 2x-1 \right)\left( x+3 \right)=0
\end{align}$
Therefore,, $ x=2,\frac{1}{2},-3$.
Thus, the solution of the equation is $ x=\left\{ \underline{-3,2,\frac{1}{2}} \right\}$.
