Solve for I
\left\{\begin{matrix}I=-\frac{5t-D-30}{5st^{2}}\text{, }&s\neq 0\text{ and }t\neq 0\\I\in \mathrm{R}\text{, }&\left(D=-30\text{ and }t=0\right)\text{ or }\left(D=5t-30\text{ and }s=0\right)\end{matrix}\right.
Solve for D
D=5\left(Ist^{2}+t-6\right)
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-30+5t+5t^{2}sI=D
Swap sides so that all variable terms are on the left hand side.
5t+5t^{2}sI=D+30
Add 30 to both sides.
5t^{2}sI=D+30-5t
Subtract 5t from both sides.
5st^{2}I=30+D-5t
The equation is in standard form.
\frac{5st^{2}I}{5st^{2}}=\frac{30+D-5t}{5st^{2}}
Divide both sides by 5t^{2}s.
I=\frac{30+D-5t}{5st^{2}}
Dividing by 5t^{2}s undoes the multiplication by 5t^{2}s.
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