#### Answer

The solution set is \[\varnothing \](the empty set

#### Work Step by Step

The equation is \[5-12x=8-7x-\left[ 6\div 3\left( 2+{{5}^{3}} \right)+5x \right]\].
Use the order of operations,
Work inside parentheses first,
\[\begin{align}
& 5-12x=8-7x-\left[ 6\div 3\left( 2+{{5}^{3}} \right)+5x \right] \\
& 5-12x=8-7x-\left[ 6\div 3\left( 2+125 \right)+5x \right] \\
& 5-12x=8-7x-\left[ 6\div 3\times 127+5x \right] \\
& 5-12x=8-7x-\left[ 2\times 127+5x \right]
\end{align}\]
\[\begin{align}
& 5-12x=8-7x-\left[ 254+5x \right] \\
& 5-12x=8-7x-254-5x \\
& 5-12x=-246-12x \\
\end{align}\]
Add \[12x\] to both sides of the equal sign,
\[\begin{align}
& 5-12x+12x=-246-12x+12x \\
& 5=-246
\end{align}\]
Therefore, the equation\[5-12x=8-7x-\left[ 6\div 3\left( 2+{{5}^{3}} \right)+5x \right]\]is equivalent to the statement \[5=-246\].
Which is false for every value of \[x\].
Thus, the equation has no solution. The solution set is \[\varnothing \](the empty set