Solve for V (complex solution)
\left\{\begin{matrix}V=0\text{, }&v\neq 0\\V\in \mathrm{C}\text{, }&r=0\text{ and }v\neq 0\end{matrix}\right.
Solve for r (complex solution)
\left\{\begin{matrix}r=0\text{, }&v\neq 0\\r\in \mathrm{C}\text{, }&V=0\text{ and }v\neq 0\end{matrix}\right.
Solve for V
\left\{\begin{matrix}V=0\text{, }&v\neq 0\\V\in \mathrm{R}\text{, }&r=0\text{ and }v\neq 0\end{matrix}\right.
Solve for r
\left\{\begin{matrix}r=0\text{, }&v\neq 0\\r\in \mathrm{R}\text{, }&V=0\text{ and }v\neq 0\end{matrix}\right.
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\epsilon \times 0v=\left(r\times 1+0\right)V
Multiply both sides of the equation by v.
0=\left(r\times 1+0\right)V
Anything times zero gives zero.
0=r\times 1V
Anything plus zero gives itself.
r\times 1V=0
Swap sides so that all variable terms are on the left hand side.
Vr=0
Reorder the terms.
rV=0
The equation is in standard form.
V=0
Divide 0 by r.
\epsilon \times 0v=\left(r\times 1+0\right)V
Multiply both sides of the equation by v.
0=\left(r\times 1+0\right)V
Anything times zero gives zero.
0=r\times 1V
Anything plus zero gives itself.
r\times 1V=0
Swap sides so that all variable terms are on the left hand side.
Vr=0
Reorder the terms.
r=0
Divide 0 by V.
\epsilon \times 0v=\left(r\times 1+0\right)V
Multiply both sides of the equation by v.
0=\left(r\times 1+0\right)V
Anything times zero gives zero.
0=r\times 1V
Anything plus zero gives itself.
r\times 1V=0
Swap sides so that all variable terms are on the left hand side.
Vr=0
Reorder the terms.
rV=0
The equation is in standard form.
V=0
Divide 0 by r.
\epsilon \times 0v=\left(r\times 1+0\right)V
Multiply both sides of the equation by v.
0=\left(r\times 1+0\right)V
Anything times zero gives zero.
0=r\times 1V
Anything plus zero gives itself.
r\times 1V=0
Swap sides so that all variable terms are on the left hand side.
Vr=0
Reorder the terms.
r=0
Divide 0 by V.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}