Answer
\[\left\{ -2 \right\}\]
Work Step by Step
The equation is\[4x+13-\left\{ 2x-\left[ 4\left( x-3 \right)-5 \right] \right\}=2\left( x-6 \right)\].
Use the order of operations,
\[\begin{align}
& 4x+13-\left\{ 2x-\left[ 4\left( x-3 \right)-5 \right] \right\}=2\left( x-6 \right) \\
& 4x+13-\left\{ 2x-\left[ 4x-12-5 \right] \right\}=2x-12 \\
& 4x+13-\left\{ 2x-\left[ 4x-17 \right] \right\}=2x-12 \\
& 4x+13-\left\{ 2x-4x+17 \right\}=2x-12
\end{align}\]
Further simplification,
\[\begin{align}
& 4x+13-\left\{ -2x+17 \right\}=2x-12 \\
& 4x+13+2x-17=2x-12 \\
& 6x-4=2x-12
\end{align}\]
Subtract \[2x\] from both sides of the equal sign,
\[\begin{align}
& 6x-4-2x=2x-12-2x \\
& 4x-4=-12
\end{align}\]
Add\[4\]to both sides of the equal sign,
\[\begin{align}
& 4x-4+4=-12+4 \\
& 4x=-8 \\
& x=\frac{-8}{4} \\
& x=-2
\end{align}\]
Therefore, \[x=-2\]
Solution set of the equation \[4x+13-\left\{ 2x-\left[ 4\left( x-3 \right)-5 \right] \right\}=2\left( x-6 \right)\]is \[\left\{ -2 \right\}\].
