Given a formula with variables, how can I turn it around to find another solution First of all, sorry for the crappy title, I have no idea how to ask this question.
I have a formula:
$$S = \left(\frac{T\cdot D\cdot C}{1000}+V^{\frac13}\right)^3$$
I now need to turn it around to find $D$, when I have $S$. I don't even know where to start. Any pointers in the right direction, or even better, the formula to find $D$ would be much appreciated.
 A: You begin with the following equation:
$$S=\left(\frac{TDC}{1000}+\sqrt[3]{V}\right)^{3}$$
You then move from the last-operation on the left-hand side inwards and perform the inverse operation on both sides, for instance, the last operation to be performed is to cube everything in the brackets, so you take the cube root of both sides to give:
$$\sqrt[3]{S}=\frac{TDC}{1000}+\sqrt[3]{V}$$
We then try and isolate the $D$ term, so our next step is to remove $\sqrt[3]{V}$ from the right-hand side by subtracting $\sqrt[3]{V}$ from both sides of the equation:
$$\sqrt[3]{S}-\sqrt[3]{V}=\frac{TDC}{1000}$$
We then multiply both sides by $1000$ to give:
$$1000(\sqrt[3]{S}-\sqrt[3]{V})=TDC$$
Dividing both sides by $TC$, we get:
$$D=\frac{1000(\sqrt[3]{S}-\sqrt[3]{V})}{TC}$$
A: Given $S = (\frac{TDC}{1000} + \sqrt[3]V)^3$ right? That's just my interpretation.
$\sqrt[3]S = \frac{TDC}{1000} + \sqrt[3]V$
$\sqrt[3]S - \sqrt[3]V = \frac{TDC}{1000}$
Next, we multiply by $\frac{1000}{TC}$
Which gives us $\displaystyle D = \frac{1000(\sqrt[3]S - \sqrt[3]V)}{TC}$
Hope that helps!
