Solve x-x_{0}=t*(frac{2V_{0}+V-V_{0}}{2})

$$x - x _ { 0 } = t \cdot ( \frac { 2 V _ { 0 } + V - V _ { 0 } } { 2 } )$$

Solve for V (complex solution)

$$\left\{\begin{matrix}V=-\frac{V_{0}t+2x_{0}-2x}{t}\text{, }&t\neq 0\\V\in \mathrm{C}\text{, }&x=x_{0}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x-2x_{0}=t\left(2V_{0}+V-V_{0}\right)$$

Combine 2V_{0} and -V_{0} to get V_{0}.

$$2x-2x_{0}=t\left(V_{0}+V\right)$$

Use the distributive property to multiply t by V_{0}+V.

$$2x-2x_{0}=tV_{0}+tV$$

Swap sides so that all variable terms are on the left hand side.

$$tV_{0}+tV=2x-2x_{0}$$

Subtract tV_{0} from both sides.

$$tV=2x-2x_{0}-tV_{0}$$

The equation is in standard form.

$$tV=2x-2x_{0}-V_{0}t$$

Divide both sides by t.

$$\frac{tV}{t}=\frac{2x-2x_{0}-V_{0}t}{t}$$

Dividing by t undoes the multiplication by t.

$$V=\frac{2x-2x_{0}-V_{0}t}{t}$$

Solve for V_0 (complex solution)

$$\left\{\begin{matrix}V_{0}=-\frac{Vt+2x_{0}-2x}{t}\text{, }&t\neq 0\\V_{0}\in \mathrm{C}\text{, }&x=x_{0}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x-2x_{0}=t\left(2V_{0}+V-V_{0}\right)$$

Combine 2V_{0} and -V_{0} to get V_{0}.

$$2x-2x_{0}=t\left(V_{0}+V\right)$$

Use the distributive property to multiply t by V_{0}+V.

$$2x-2x_{0}=tV_{0}+tV$$

Swap sides so that all variable terms are on the left hand side.

$$tV_{0}+tV=2x-2x_{0}$$

Subtract tV from both sides.

$$tV_{0}=2x-2x_{0}-tV$$

The equation is in standard form.

$$tV_{0}=2x-2x_{0}-Vt$$

Divide both sides by t.

$$\frac{tV_{0}}{t}=\frac{2x-2x_{0}-Vt}{t}$$

Dividing by t undoes the multiplication by t.

$$V_{0}=\frac{2x-2x_{0}-Vt}{t}$$

Solve for V

$$\left\{\begin{matrix}V=-\frac{V_{0}t+2x_{0}-2x}{t}\text{, }&t\neq 0\\V\in \mathrm{R}\text{, }&x=x_{0}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x-2x_{0}=t\left(2V_{0}+V-V_{0}\right)$$

Combine 2V_{0} and -V_{0} to get V_{0}.

$$2x-2x_{0}=t\left(V_{0}+V\right)$$

Use the distributive property to multiply t by V_{0}+V.

$$2x-2x_{0}=tV_{0}+tV$$

Swap sides so that all variable terms are on the left hand side.

$$tV_{0}+tV=2x-2x_{0}$$

Subtract tV_{0} from both sides.

$$tV=2x-2x_{0}-tV_{0}$$

The equation is in standard form.

$$tV=2x-2x_{0}-V_{0}t$$

Divide both sides by t.

$$\frac{tV}{t}=\frac{2x-2x_{0}-V_{0}t}{t}$$

Dividing by t undoes the multiplication by t.

$$V=\frac{2x-2x_{0}-V_{0}t}{t}$$

Solve for V_0

$$\left\{\begin{matrix}V_{0}=-\frac{Vt+2x_{0}-2x}{t}\text{, }&t\neq 0\\V_{0}\in \mathrm{R}\text{, }&x=x_{0}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x-2x_{0}=t\left(2V_{0}+V-V_{0}\right)$$

Combine 2V_{0} and -V_{0} to get V_{0}.

$$2x-2x_{0}=t\left(V_{0}+V\right)$$

Use the distributive property to multiply t by V_{0}+V.

$$2x-2x_{0}=tV_{0}+tV$$

Swap sides so that all variable terms are on the left hand side.

$$tV_{0}+tV=2x-2x_{0}$$

Subtract tV from both sides.

$$tV_{0}=2x-2x_{0}-tV$$

The equation is in standard form.

$$tV_{0}=2x-2x_{0}-Vt$$

Divide both sides by t.

$$\frac{tV_{0}}{t}=\frac{2x-2x_{0}-Vt}{t}$$

Dividing by t undoes the multiplication by t.

$$V_{0}=\frac{2x-2x_{0}-Vt}{t}$$