Solve y=sqrt[3]{x^2-13}a

$$y = \sqrt[ 3 ] { x ^ { 2 } - 13 } a$$

Solve for a

$$\left\{\begin{matrix}a=\frac{y}{\sqrt[3]{x^{2}-13}}\text{, }&|x|\neq \sqrt{13}\\a\in \mathrm{R}\text{, }&y=0\text{ and }|x|=\sqrt{13}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\sqrt[3]{x^{2}-13}a=y$$

Divide both sides by \sqrt[3]{x^{2}-13}.

$$\frac{\sqrt[3]{x^{2}-13}a}{\sqrt[3]{x^{2}-13}}=\frac{y}{\sqrt[3]{x^{2}-13}}$$

Dividing by \sqrt[3]{x^{2}-13} undoes the multiplication by \sqrt[3]{x^{2}-13}.

$$a=\frac{y}{\sqrt[3]{x^{2}-13}}$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\left(\frac{y}{a}\right)^{3}+13}\text{; }x=-\sqrt{\left(\frac{y}{a}\right)^{3}+13}\text{, }&\left(a<0\text{ or }y\geq -\sqrt[3]{13}a\right)\text{ and }\left(a>0\text{ or }y\leq -\sqrt[3]{13}a\right)\text{ and }a\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$