Solve y=p^2x+p

$$y = p ^ { 2 } x + p$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{p-y}{p^{2}}\text{, }&p\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$p^{2}x+p=y$$

Subtract p from both sides.

$$p^{2}x=y-p$$

Divide both sides by p^{2}.

$$\frac{p^{2}x}{p^{2}}=\frac{y-p}{p^{2}}$$

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

$$x=\frac{y-p}{p^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{p-y}{p^{2}}\text{, }&p\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$p^{2}x+p=y$$

Subtract p from both sides.

$$p^{2}x=y-p$$

Divide both sides by p^{2}.

$$\frac{p^{2}x}{p^{2}}=\frac{y-p}{p^{2}}$$

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

$$x=\frac{y-p}{p^{2}}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{\sqrt{4xy+1}+1}{2x}\text{; }p=-\frac{-\sqrt{4xy+1}+1}{2x}\text{, }&x\neq 0\\p=y\text{, }&x=0\end{matrix}\right.$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{\sqrt{4xy+1}+1}{2x}\text{; }p=-\frac{-\sqrt{4xy+1}+1}{2x}\text{, }&\left(y\leq -\frac{1}{4x}\text{ and }x<0\right)\text{ or }\left(y\geq -\frac{1}{4x}\text{ and }x>0\right)\text{ or }\left(x\neq 0\text{ and }y=-\frac{1}{4x}\right)\\p=y\text{, }&x=0\end{matrix}\right.$$