Solve y=a^2(t-1)

$$y = a ^ { 2 } ( t - 1 )$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=1+\frac{y}{a^{2}}\text{, }&a\neq 0\\t\in \mathrm{C}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a^{2} by t-1.

$$y=a^{2}t-a^{2}$$

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

$$a^{2}t-a^{2}=y$$

Add a^{2} to both sides.

$$a^{2}t=y+a^{2}$$

Divide both sides by a^{2}.

$$\frac{a^{2}t}{a^{2}}=\frac{y+a^{2}}{a^{2}}$$

Dividing by a^{2} undoes the multiplication by a^{2}.

$$t=\frac{y+a^{2}}{a^{2}}$$

Divide y+a^{2} by a^{2}.

$$t=1+\frac{y}{a^{2}}$$

Solve for t

$$\left\{\begin{matrix}t=1+\frac{y}{a^{2}}\text{, }&a\neq 0\\t\in \mathrm{R}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a^{2} by t-1.

$$y=a^{2}t-a^{2}$$

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

$$a^{2}t-a^{2}=y$$

Add a^{2} to both sides.

$$a^{2}t=y+a^{2}$$

Divide both sides by a^{2}.

$$\frac{a^{2}t}{a^{2}}=\frac{y+a^{2}}{a^{2}}$$

Dividing by a^{2} undoes the multiplication by a^{2}.

$$t=\frac{y+a^{2}}{a^{2}}$$

Divide y+a^{2} by a^{2}.

$$t=1+\frac{y}{a^{2}}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-i\left(1-t\right)^{-\frac{1}{2}}\sqrt{y}\text{; }a=i\left(1-t\right)^{-\frac{1}{2}}\sqrt{y}\text{, }&t\neq 1\\a\in \mathrm{C}\text{, }&y=0\text{ and }t=1\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=\sqrt{-\frac{y}{1-t}}\text{; }a=-\sqrt{-\frac{y}{1-t}}\text{, }&\left(y\leq 0\text{ and }t<1\right)\text{ or }\left(y\geq 0\text{ and }t>1\right)\\a\in \mathrm{R}\text{, }&y=0\text{ and }t=1\end{matrix}\right.$$