Solve y^2+(x-y)b-x=0

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

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

$$y^{2}+xb-yb-x=0$$

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

$$xb-yb-x=-y^{2}$$

Add x to both sides.

$$xb-yb=-y^{2}+x$$

Combine all terms containing b.

$$\left(x-y\right)b=-y^{2}+x$$

The equation is in standard form.

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

Divide both sides by x-y.

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

Dividing by x-y undoes the multiplication by x-y.

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$y^{2}+xb-yb-x=0$$

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

$$xb-yb-x=-y^{2}$$

Add yb to both sides.

$$xb-x=-y^{2}+yb$$

Combine all terms containing x.

$$\left(b-1\right)x=-y^{2}+yb$$

The equation is in standard form.

$$\left(b-1\right)x=by-y^{2}$$

Divide both sides by b-1.

$$\frac{\left(b-1\right)x}{b-1}=\frac{y\left(b-y\right)}{b-1}$$

Dividing by b-1 undoes the multiplication by b-1.

$$x=\frac{y\left(b-y\right)}{b-1}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{y^{2}-x}{x-y}\text{, }&y\neq x\\b\in \mathrm{R}\text{, }&\left(x=0\text{ and }y=0\right)\text{ or }\left(x=1\text{ and }y=1\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y^{2}+xb-yb-x=0$$

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

$$xb-yb-x=-y^{2}$$

Add x to both sides.

$$xb-yb=-y^{2}+x$$

Combine all terms containing b.

$$\left(x-y\right)b=-y^{2}+x$$

The equation is in standard form.

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

Divide both sides by x-y.

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

Dividing by x-y undoes the multiplication by x-y.

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

Solve for x

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

Steps for Solving Linear Equation

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

$$y^{2}+xb-yb-x=0$$

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

$$xb-yb-x=-y^{2}$$

Add yb to both sides.

$$xb-x=-y^{2}+yb$$

Combine all terms containing x.

$$\left(b-1\right)x=-y^{2}+yb$$

The equation is in standard form.

$$\left(b-1\right)x=by-y^{2}$$

Divide both sides by b-1.

$$\frac{\left(b-1\right)x}{b-1}=\frac{y\left(b-y\right)}{b-1}$$

Dividing by b-1 undoes the multiplication by b-1.

$$x=\frac{y\left(b-y\right)}{b-1}$$