Solve yp^2+(x-y)p-x=0

$$y p ^ { 2 } + ( x - y ) p - x = 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-py\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&p=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-y by p.

$$yp^{2}+xp-yp-x=0$$

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

$$xp-yp-x=-yp^{2}$$

Add yp to both sides.

$$xp-x=-yp^{2}+yp$$

Reorder the terms.

$$px-x=py-yp^{2}$$

Combine all terms containing x.

$$\left(p-1\right)x=py-yp^{2}$$

Divide both sides by -1+p.

$$\frac{\left(p-1\right)x}{p-1}=\frac{py\left(1-p\right)}{p-1}$$

Dividing by -1+p undoes the multiplication by -1+p.

$$x=\frac{py\left(1-p\right)}{p-1}$$

Divide yp\left(1-p\right) by -1+p.

$$x=-py$$

Solve for x

$$\left\{\begin{matrix}\\x=-py\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&p=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-y by p.

$$yp^{2}+xp-yp-x=0$$

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

$$xp-yp-x=-yp^{2}$$

Add yp to both sides.

$$xp-x=-yp^{2}+yp$$

Reorder the terms.

$$px-x=py-yp^{2}$$

Combine all terms containing x.

$$\left(p-1\right)x=py-yp^{2}$$

Divide both sides by -1+p.

$$\frac{\left(p-1\right)x}{p-1}=\frac{py\left(1-p\right)}{p-1}$$

Dividing by -1+p undoes the multiplication by -1+p.

$$x=\frac{py\left(1-p\right)}{p-1}$$

Divide yp\left(1-p\right) by -1+p.

$$x=-py$$

Solve for p (complex solution)

$$\left\{\begin{matrix}\\p=1\text{, }&\text{unconditionally}\\p=-\frac{x}{y}\text{, }&y\neq 0\\p\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Solve for p

$$\left\{\begin{matrix}\\p=1\text{, }&\text{unconditionally}\\p=-\frac{x}{y}\text{, }&y\neq 0\\p\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$