Solve x(x-a)+y(y-c)=0

$$x ( x - a ) + y ( y - c ) = 0$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply x by x-a.

$$x^{2}-xa+y\left(y-c\right)=0$$

Use the distributive property to multiply y by y-c.

$$x^{2}-xa+y^{2}-yc=0$$

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

$$-xa+y^{2}-yc=-x^{2}$$

Subtract y^{2} from both sides.

$$-xa-yc=-x^{2}-y^{2}$$

Add yc to both sides.

$$-xa=-x^{2}-y^{2}+yc$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

$$a=\frac{cy-y^{2}-x^{2}}{-x}$$

Divide -x^{2}-y^{2}+cy by -x.

$$a=\frac{y^{2}-cy}{x}+x$$

Solve for c (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply x by x-a.

$$x^{2}-xa+y\left(y-c\right)=0$$

Use the distributive property to multiply y by y-c.

$$x^{2}-xa+y^{2}-yc=0$$

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

$$-xa+y^{2}-yc=-x^{2}$$

Add xa to both sides.

$$y^{2}-yc=-x^{2}+xa$$

Subtract y^{2} from both sides.

$$-yc=-x^{2}+xa-y^{2}$$

The equation is in standard form.

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

Divide both sides by -y.

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

Dividing by -y undoes the multiplication by -y.

$$c=\frac{ax-y^{2}-x^{2}}{-y}$$

Divide -x^{2}-y^{2}+xa by -y.

$$c=\frac{x^{2}-ax}{y}+y$$

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply x by x-a.

$$x^{2}-xa+y\left(y-c\right)=0$$

Use the distributive property to multiply y by y-c.

$$x^{2}-xa+y^{2}-yc=0$$

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

$$-xa+y^{2}-yc=-x^{2}$$

Subtract y^{2} from both sides.

$$-xa-yc=-x^{2}-y^{2}$$

Add yc to both sides.

$$-xa=-x^{2}-y^{2}+yc$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

$$a=\frac{cy-y^{2}-x^{2}}{-x}$$

Divide -x^{2}-y^{2}+yc by -x.

$$a=\frac{y^{2}-cy}{x}+x$$

Solve for c

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

Steps for Solving Linear Equation

Use the distributive property to multiply x by x-a.

$$x^{2}-xa+y\left(y-c\right)=0$$

Use the distributive property to multiply y by y-c.

$$x^{2}-xa+y^{2}-yc=0$$

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

$$-xa+y^{2}-yc=-x^{2}$$

Add xa to both sides.

$$y^{2}-yc=-x^{2}+xa$$

Subtract y^{2} from both sides.

$$-yc=-x^{2}+xa-y^{2}$$

The equation is in standard form.

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

Divide both sides by -y.

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

Dividing by -y undoes the multiplication by -y.

$$c=\frac{ax-y^{2}-x^{2}}{-y}$$

Divide -x^{2}+xa-y^{2} by -y.

$$c=\frac{x^{2}-ax}{y}+y$$