Solve x=sw-sc^3

$$x = s w - s c ^ { 3 }$$

Solve for s (complex solution)

$$\left\{\begin{matrix}s=\frac{x}{w-c^{3}}\text{, }&w\neq c^{3}\\s\in \mathrm{C}\text{, }&x=0\text{ and }w=c^{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$sw-sc^{3}=x$$

Reorder the terms.

$$-sc^{3}+sw=x$$

Combine all terms containing s.

$$\left(-c^{3}+w\right)s=x$$

The equation is in standard form.

$$\left(w-c^{3}\right)s=x$$

Divide both sides by w-c^{3}.

$$\frac{\left(w-c^{3}\right)s}{w-c^{3}}=\frac{x}{w-c^{3}}$$

Dividing by w-c^{3} undoes the multiplication by w-c^{3}.

$$s=\frac{x}{w-c^{3}}$$

Solve for s

$$\left\{\begin{matrix}s=\frac{x}{w-c^{3}}\text{, }&w\neq c^{3}\\s\in \mathrm{R}\text{, }&x=0\text{ and }w=c^{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$sw-sc^{3}=x$$

Reorder the terms.

$$-sc^{3}+sw=x$$

Combine all terms containing s.

$$\left(-c^{3}+w\right)s=x$$

The equation is in standard form.

$$\left(w-c^{3}\right)s=x$$

Divide both sides by w-c^{3}.

$$\frac{\left(w-c^{3}\right)s}{w-c^{3}}=\frac{x}{w-c^{3}}$$

Dividing by w-c^{3} undoes the multiplication by w-c^{3}.

$$s=\frac{x}{w-c^{3}}$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=e^{\frac{2\pi i}{3}}\sqrt[3]{w-\frac{x}{s}}\text{; }c=\sqrt[3]{w-\frac{x}{s}}\text{; }c=e^{\frac{4\pi i}{3}}\sqrt[3]{w-\frac{x}{s}}\text{, }&s\neq 0\\c\in \mathrm{C}\text{, }&x=0\text{ and }s=0\end{matrix}\right.$$

Solve for c

$$\left\{\begin{matrix}c=\sqrt[3]{w-\frac{x}{s}}\text{, }&s\neq 0\\c\in \mathrm{R}\text{, }&x=0\text{ and }s=0\end{matrix}\right.$$