\frac { d } { d x } 3 x ^ { 2 } + 2 d x = 0
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.
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2dx=-\frac{\mathrm{d}}{\mathrm{d}x}(3)x^{2}
Subtract \frac{\mathrm{d}}{\mathrm{d}x}(3)x^{2} from both sides. Anything subtracted from zero gives its negation.
2dx=-x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(3)
Reorder the terms.
2xd=0
The equation is in standard form.
d=0
Divide 0 by 2x.
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