Solve m2d(c^2-v^2)/dv+dm^2/dv(c^2-v)=0

$$m \frac { 2 d ( c ^ { 2 } - v ^ { 2 } ) } { d v } + \frac { d m ^ { 2 } } { d v } ( c ^ { 2 } - v ) = 0$$

Solve for d (complex solution)

$$d\neq 0$$

$$\left(v\neq 0\text{ and }c=-v\right)\text{ or }\left(v=c\text{ and }c\neq 0\right)\text{ or }\left(m=0\text{ and }v\neq 0\right)$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dv.

$$m\times 2d\left(c^{2}-v^{2}\right)+\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}\left(c^{2}-v\right)dv=0$$

Use the distributive property to multiply m\times 2d by c^{2}-v^{2}.

$$2mdc^{2}-2v^{2}md+\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}\left(c^{2}-v\right)dv=0$$

Use the distributive property to multiply \frac{\mathrm{d}(m^{2})}{\mathrm{d}v} by c^{2}-v.

$$2mdc^{2}-2v^{2}md+\left(\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}v\right)dv=0$$

Use the distributive property to multiply \frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}v by d.

$$2mdc^{2}-2v^{2}md+\left(\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}d-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}vd\right)v=0$$

Use the distributive property to multiply \frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}d-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}vd by v.

$$2mdc^{2}-2v^{2}md+\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}dv-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}dv^{2}=0$$

Combine all terms containing d.

$$\left(2mc^{2}-2v^{2}m+\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}v-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}v^{2}\right)d=0$$

The equation is in standard form.

$$\left(2mc^{2}-2mv^{2}\right)d=0$$

Divide 0 by 2mc^{2}-2v^{2}m.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for d

$$d\neq 0$$

$$\left(m=0\text{ or }|c|=|v|\right)\text{ and }v\neq 0$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dv.

$$m\times 2d\left(c^{2}-v^{2}\right)+\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}\left(c^{2}-v\right)dv=0$$

Use the distributive property to multiply m\times 2d by c^{2}-v^{2}.

$$2mdc^{2}-2v^{2}md+\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}\left(c^{2}-v\right)dv=0$$

Use the distributive property to multiply \frac{\mathrm{d}(m^{2})}{\mathrm{d}v} by c^{2}-v.

$$2mdc^{2}-2v^{2}md+\left(\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}v\right)dv=0$$

Use the distributive property to multiply \frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}v by d.

$$2mdc^{2}-2v^{2}md+\left(\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}d-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}vd\right)v=0$$

Use the distributive property to multiply \frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}d-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}vd by v.

$$2mdc^{2}-2v^{2}md+\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}dv-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}dv^{2}=0$$

Combine all terms containing d.

$$\left(2mc^{2}-2v^{2}m+\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}c^{2}v-\frac{\mathrm{d}(m^{2})}{\mathrm{d}v}v^{2}\right)d=0$$

The equation is in standard form.

$$\left(2mc^{2}-2mv^{2}\right)d=0$$

Divide 0 by 2mc^{2}-2v^{2}m.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=-v\text{; }c=v\text{, }&d\neq 0\text{ and }v\neq 0\\c\in \mathrm{C}\text{, }&m=0\text{ and }v\neq 0\text{ and }d\neq 0\end{matrix}\right.$$

Solve for c

$$\left\{\begin{matrix}c=v\text{; }c=-v\text{, }&m\neq 0\text{ and }v\neq 0\text{ and }d\neq 0\\c\in \mathrm{R}\text{, }&m=0\text{ and }v\neq 0\text{ and }d\neq 0\end{matrix}\right.$$