solve for LD: w = 0.002(2000-LD)

solve for LD: w = 0.002(2000-LD)

Having some trouble with this one, the LD equation I'm getting has some interesting signs (I get LD = -2000-500w) which I don't think makes intuitive sense.

$\begin{array}{rcll} w &=& 0.002\cdot (2000-LD) \qquad &|\qquad :0.002\\\\ \dfrac{w}{0.002} &=& 2000-LD \qquad &|\qquad +LD\\\\ LD + \dfrac{w}{0.002} &=& 2000 \qquad &|\qquad - \dfrac{w}{0.002}\\\\ LD &=& 2000 - \dfrac{w}{0.002}\\\\ LD &=& 2000 - \dfrac{1}{0.002}\cdot w\\\\ LD &=& 2000 - \dfrac{1}{\frac{2}{1000}}\cdot w\\\\ LD &=& 2000 - \dfrac{1000}{2}\cdot w\\\\ \mathbf{LD} &\mathbf{=}& \mathbf{2000 - 500\cdot w} \end{array}$