Solve vO_{2}=50x(3-x^2)

$$v O _ { 2 } = 50 x ( 3 - x ^ { 2 } )$$

Solve for O_2 (complex solution)

$$\left\{\begin{matrix}O_{2}=-\frac{50x\left(x^{2}-3\right)}{v}\text{, }&v\neq 0\\O_{2}\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=\sqrt{3}\text{ or }x=-\sqrt{3}\right)\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 50x by 3-x^{2}.

$$vO_{2}=150x-50x^{3}$$

Divide both sides by v.

$$\frac{vO_{2}}{v}=\frac{150x-50x^{3}}{v}$$

Dividing by v undoes the multiplication by v.

$$O_{2}=\frac{150x-50x^{3}}{v}$$

Divide 150x-50x^{3} by v.

$$O_{2}=\frac{50x\left(3-x^{2}\right)}{v}$$

Solve for v (complex solution)

$$\left\{\begin{matrix}v=-\frac{50x\left(x^{2}-3\right)}{O_{2}}\text{, }&O_{2}\neq 0\\v\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=\sqrt{3}\text{ or }x=-\sqrt{3}\right)\text{ and }O_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 50x by 3-x^{2}.

$$vO_{2}=150x-50x^{3}$$

The equation is in standard form.

$$O_{2}v=150x-50x^{3}$$

Divide both sides by O_{2}.

$$\frac{O_{2}v}{O_{2}}=\frac{150x-50x^{3}}{O_{2}}$$

Dividing by O_{2} undoes the multiplication by O_{2}.

$$v=\frac{150x-50x^{3}}{O_{2}}$$

Divide 150x-50x^{3} by O_{2}.

$$v=\frac{50x\left(3-x^{2}\right)}{O_{2}}$$

Solve for O_2

$$\left\{\begin{matrix}O_{2}=-\frac{50x\left(x^{2}-3\right)}{v}\text{, }&v\neq 0\\O_{2}\in \mathrm{R}\text{, }&\left(x=0\text{ or }|x|=\sqrt{3}\right)\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 50x by 3-x^{2}.

$$vO_{2}=150x-50x^{3}$$

Divide both sides by v.

$$\frac{vO_{2}}{v}=\frac{150x-50x^{3}}{v}$$

Dividing by v undoes the multiplication by v.

$$O_{2}=\frac{150x-50x^{3}}{v}$$

Divide 150x-50x^{3} by v.

$$O_{2}=\frac{50x\left(3-x^{2}\right)}{v}$$

Solve for v

$$\left\{\begin{matrix}v=-\frac{50x\left(x^{2}-3\right)}{O_{2}}\text{, }&O_{2}\neq 0\\v\in \mathrm{R}\text{, }&\left(x=0\text{ or }|x|=\sqrt{3}\right)\text{ and }O_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 50x by 3-x^{2}.

$$vO_{2}=150x-50x^{3}$$

The equation is in standard form.

$$O_{2}v=150x-50x^{3}$$

Divide both sides by O_{2}.

$$\frac{O_{2}v}{O_{2}}=\frac{150x-50x^{3}}{O_{2}}$$

Dividing by O_{2} undoes the multiplication by O_{2}.

$$v=\frac{150x-50x^{3}}{O_{2}}$$

Divide 150x-50x^{3} by O_{2}.

$$v=\frac{50x\left(3-x^{2}\right)}{O_{2}}$$