\(5x-\left\{4x-2\left[4x-3\left(5x-2\right)\right]\right\}=182\)
\(5x-\left[4x-2\left(4x-15x+6\right)\right]=182\)
\(5x-\left[4x-2\left(-11x+6\right)\right]=182\)
\(5x-\left(4x+22x-12\right)=182\)
\(5x-\left(26x-12\right)=182\)
\(5x-26x+12=182\)
\(-21x=182-12\)
\(-21x=170\)
\(x=-\frac{170}{21}\)