Solve y(1-p^2)(1+x%)=y

$$y ( 1 - p ^ { 2 } ) ( 1 + x \% ) = y$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{100p^{2}}{1-p^{2}}\text{, }&p\neq 1\text{ and }p\neq -1\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by 1-p^{2}.

$$\left(y-yp^{2}\right)\left(1+\frac{x}{100}\right)=y$$

Use the distributive property to multiply y-yp^{2} by 1+\frac{x}{100}.

$$y+y\times \frac{x}{100}-yp^{2}-yp^{2}\times \frac{x}{100}=y$$

Express y\times \frac{x}{100} as a single fraction.

$$y+\frac{yx}{100}-yp^{2}-yp^{2}\times \frac{x}{100}=y$$

Express y\times \frac{x}{100} as a single fraction.

$$y+\frac{yx}{100}-yp^{2}-\frac{yx}{100}p^{2}=y$$

Express \frac{yx}{100}p^{2} as a single fraction.

$$y+\frac{yx}{100}-yp^{2}-\frac{yxp^{2}}{100}=y$$

Subtract y from both sides.

$$\frac{yx}{100}-yp^{2}-\frac{yxp^{2}}{100}=y-y$$

Since \frac{yx}{100} and \frac{yxp^{2}}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{yx-yxp^{2}}{100}-yp^{2}=y-y$$

Combine y and -y to get 0.

$$\frac{yx-yxp^{2}}{100}-yp^{2}=0$$

Add yp^{2} to both sides. Anything plus zero gives itself.

$$\frac{yx-yxp^{2}}{100}=yp^{2}$$

Multiply both sides of the equation by 100.

$$yx-yxp^{2}=100yp^{2}$$

Combine all terms containing x.

$$\left(y-yp^{2}\right)x=100yp^{2}$$

Divide both sides by y-yp^{2}.

$$\frac{\left(y-yp^{2}\right)x}{y-yp^{2}}=\frac{100yp^{2}}{y-yp^{2}}$$

Dividing by y-yp^{2} undoes the multiplication by y-yp^{2}.

$$x=\frac{100yp^{2}}{y-yp^{2}}$$

Divide 100yp^{2} by y-yp^{2}.

$$x=\frac{100p^{2}}{1-p^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{100p^{2}}{1-p^{2}}\text{, }&|p|\neq 1\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by 1-p^{2}.

$$\left(y-yp^{2}\right)\left(1+\frac{x}{100}\right)=y$$

Use the distributive property to multiply y-yp^{2} by 1+\frac{x}{100}.

$$y+y\times \frac{x}{100}-yp^{2}-yp^{2}\times \frac{x}{100}=y$$

Express y\times \frac{x}{100} as a single fraction.

$$y+\frac{yx}{100}-yp^{2}-yp^{2}\times \frac{x}{100}=y$$

Express y\times \frac{x}{100} as a single fraction.

$$y+\frac{yx}{100}-yp^{2}-\frac{yx}{100}p^{2}=y$$

Express \frac{yx}{100}p^{2} as a single fraction.

$$y+\frac{yx}{100}-yp^{2}-\frac{yxp^{2}}{100}=y$$

Subtract y from both sides.

$$\frac{yx}{100}-yp^{2}-\frac{yxp^{2}}{100}=y-y$$

Since \frac{yx}{100} and \frac{yxp^{2}}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{yx-yxp^{2}}{100}-yp^{2}=y-y$$

Combine y and -y to get 0.

$$\frac{yx-yxp^{2}}{100}-yp^{2}=0$$

Add yp^{2} to both sides. Anything plus zero gives itself.

$$\frac{yx-yxp^{2}}{100}=yp^{2}$$

Multiply both sides of the equation by 100.

$$yx-yxp^{2}=100yp^{2}$$

Combine all terms containing x.

$$\left(y-yp^{2}\right)x=100yp^{2}$$

Divide both sides by y-yp^{2}.

$$\frac{\left(y-yp^{2}\right)x}{y-yp^{2}}=\frac{100yp^{2}}{y-yp^{2}}$$

Dividing by y-yp^{2} undoes the multiplication by y-yp^{2}.

$$x=\frac{100yp^{2}}{y-yp^{2}}$$

Divide 100yp^{2} by y-yp^{2}.

$$x=\frac{100p^{2}}{1-p^{2}}$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-i\left(-x-100\right)^{-\frac{1}{2}}\sqrt{x}\text{; }p=i\left(-x-100\right)^{-\frac{1}{2}}\sqrt{x}\text{, }&x\neq -100\\p\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Solve for p

$$\left\{\begin{matrix}p=\sqrt{\frac{x}{x+100}}\text{; }p=-\sqrt{\frac{x}{x+100}}\text{, }&x\geq 0\text{ or }x<-100\\p\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$