Answer
The value of \[{{x}^{2}}-x\]is \[6\].
Work Step by Step
The equation \[2\left( x-6 \right)=3x+2\left( 2x-1 \right)\].
Use the distributive property, \[a\left( b+c \right)=ab+ac\].
\[\begin{align}
& 2x-12=3x+4x-2 \\
& 2x-12=7x-2 \\
\end{align}\]
Add \[2\]to both side,
\[\begin{align}
& 2x-12+2=7x-2+2 \\
& 2x-10=7x
\end{align}\]
Subtract \[2x\] from both side,
\[\begin{align}
& 2x-2x-10=7x-2x \\
& -10=5x
\end{align}\]
Divided by 5 both side,
\[\begin{align}
& \frac{-10}{5}=\frac{5x}{5} \\
& -2=x \\
& x=-2 \\
\end{align}\]
The solution set is \[\left\{ -2 \right\}\].
Check the proposed solution. Substitute \[-2\] for x in the original equation \[2\left( x-6 \right)=3x+2\left( 2x-1 \right)\].
\[\begin{align}
& 2\left( -2-6 \right)=3\left( -2 \right)+2\left( 2\left( -2 \right)-1 \right) \\
& 2\left( -8 \right)=-6+2\left( -5 \right) \\
& -16=-6-10 \\
& -16=-16
\end{align}\]
This true statement \[-16=-16\] verifies that the solution set is \[\left\{ -2 \right\}\].
Now put \[x=-2\] in the expression \[{{x}^{2}}-x\].
\[\begin{align}
& {{x}^{2}}-x={{\left( -2 \right)}^{2}}-\left( -2 \right) \\
& =4+2 \\
& =6
\end{align}\]
Therefore, value of \[{{x}^{2}}-x\]is \[6\].
