$$8(x-3)-(6-2x)=2(x+2)-5(5-x)$$
$x=3$
$$8x-24-\left(6-2x\right)=2\left(x+2\right)-5\left(5-x\right)$$
$$8x-24-6-\left(-2x\right)=2\left(x+2\right)-5\left(5-x\right)$$
$$8x-24-6+2x=2\left(x+2\right)-5\left(5-x\right)$$
$$8x-30+2x=2\left(x+2\right)-5\left(5-x\right)$$
$$10x-30=2\left(x+2\right)-5\left(5-x\right)$$
$$10x-30=2x+4-5\left(5-x\right)$$
$$10x-30=2x+4-25+5x$$
$$10x-30=2x-21+5x$$
$$10x-30=7x-21$$
$$10x-30-7x=-21$$
$$3x-30=-21$$
$$3x=-21+30$$
$$3x=9$$
$$x=\frac{9}{3}$$
$$x=3$$
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