Solve t^2-2st-t*k^2+2sk^2=0

$$t ^ { 2 } - 2 s t - t \cdot k ^ { 2 } + 2 s k ^ { 2 } = 0$$

Solve for s (complex solution)

$$\left\{\begin{matrix}\\s=\frac{t}{2}\text{, }&\text{unconditionally}\\s\in \mathrm{C}\text{, }&t=k^{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract t^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2st-tk^{2}+2sk^{2}=-t^{2}$$

Add tk^{2} to both sides.

$$-2st+2sk^{2}=-t^{2}+tk^{2}$$

Combine all terms containing s.

$$\left(-2t+2k^{2}\right)s=-t^{2}+tk^{2}$$

The equation is in standard form.

$$\left(2k^{2}-2t\right)s=tk^{2}-t^{2}$$

Divide both sides by -2t+2k^{2}.

$$\frac{\left(2k^{2}-2t\right)s}{2k^{2}-2t}=\frac{t\left(k^{2}-t\right)}{2k^{2}-2t}$$

Dividing by -2t+2k^{2} undoes the multiplication by -2t+2k^{2}.

$$s=\frac{t\left(k^{2}-t\right)}{2k^{2}-2t}$$

Divide t\left(-t+k^{2}\right) by -2t+2k^{2}.

$$s=\frac{t}{2}$$

Solve for s

$$\left\{\begin{matrix}\\s=\frac{t}{2}\text{, }&\text{unconditionally}\\s\in \mathrm{R}\text{, }&t=k^{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract t^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2st-tk^{2}+2sk^{2}=-t^{2}$$

Add tk^{2} to both sides.

$$-2st+2sk^{2}=-t^{2}+tk^{2}$$

Combine all terms containing s.

$$\left(-2t+2k^{2}\right)s=-t^{2}+tk^{2}$$

The equation is in standard form.

$$\left(2k^{2}-2t\right)s=tk^{2}-t^{2}$$

Divide both sides by -2t+2k^{2}.

$$\frac{\left(2k^{2}-2t\right)s}{2k^{2}-2t}=\frac{t\left(k^{2}-t\right)}{2k^{2}-2t}$$

Dividing by -2t+2k^{2} undoes the multiplication by -2t+2k^{2}.

$$s=\frac{t\left(k^{2}-t\right)}{2k^{2}-2t}$$

Divide t\left(-t+k^{2}\right) by -2t+2k^{2}.

$$s=\frac{t}{2}$$

Solve for k (complex solution)

$$\left\{\begin{matrix}\\k=-\sqrt{t}\text{; }k=\sqrt{t}\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&t=2s\end{matrix}\right.$$

Solve for k

$$\left\{\begin{matrix}k=\sqrt{t}\text{; }k=-\sqrt{t}\text{, }&t\geq 0\\k\in \mathrm{R}\text{, }&t=2s\end{matrix}\right.$$