Solve sinx=30000cm^3

$$\sin x = 30000 cm ^ { 3 }$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{\sin(x)}{30000m^{3}}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$30000cm^{3}=\sin(x)$$

The equation is in standard form.

$$30000m^{3}c=\sin(x)$$

Divide both sides by 30000m^{3}.

$$\frac{30000m^{3}c}{30000m^{3}}=\frac{\sin(x)}{30000m^{3}}$$

Dividing by 30000m^{3} undoes the multiplication by 30000m^{3}.

$$c=\frac{\sin(x)}{30000m^{3}}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{\sin(x)}{30000m^{3}}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$30000cm^{3}=\sin(x)$$

The equation is in standard form.

$$30000m^{3}c=\sin(x)$$

Divide both sides by 30000m^{3}.

$$\frac{30000m^{3}c}{30000m^{3}}=\frac{\sin(x)}{30000m^{3}}$$

Dividing by 30000m^{3} undoes the multiplication by 30000m^{3}.

$$c=\frac{\sin(x)}{30000m^{3}}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{\sqrt[3]{900}c^{-\frac{1}{3}}\sqrt[3]{-\sin(x)}}{300}\text{; }m=\frac{\sqrt[3]{900}e^{\frac{\pi i}{3}}c^{-\frac{1}{3}}\sqrt[3]{-\sin(x)}}{300}\text{; }m=-\frac{\sqrt[3]{900}ie^{\frac{\pi i}{6}}c^{-\frac{1}{3}}\sqrt[3]{-\sin(x)}}{300}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }c=0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\frac{30^{\frac{2}{3}}\sqrt[3]{\frac{\sin(x)}{c}}}{300}\text{, }&c\neq 0\\m\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }c=0\end{matrix}\right.$$