Solve x^2+6x-27=(x+9)(x-y)

$${ x }^{ 2 } +6x-27=(x+9)(x-y)$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-9\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+9 by x-y.

$$x^{2}+6x-27=x^{2}-xy+9x-9y$$

Subtract x^{2} from both sides.

$$x^{2}+6x-27-x^{2}=-xy+9x-9y$$

Combine x^{2} and -x^{2} to get 0.

$$6x-27=-xy+9x-9y$$

Add xy to both sides.

$$6x-27+xy=9x-9y$$

Subtract 9x from both sides.

$$6x-27+xy-9x=-9y$$

Combine 6x and -9x to get -3x.

$$-3x-27+xy=-9y$$

Add 27 to both sides.

$$-3x+xy=-9y+27$$

Combine all terms containing x.

$$\left(-3+y\right)x=-9y+27$$

The equation is in standard form.

$$\left(y-3\right)x=27-9y$$

Divide both sides by -3+y.

$$\frac{\left(y-3\right)x}{y-3}=\frac{27-9y}{y-3}$$

Dividing by -3+y undoes the multiplication by -3+y.

$$x=\frac{27-9y}{y-3}$$

Divide -9y+27 by -3+y.

$$x=-9$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=3\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=-9\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+9 by x-y.

$$x^{2}+6x-27=x^{2}-xy+9x-9y$$

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

$$x^{2}-xy+9x-9y=x^{2}+6x-27$$

Subtract x^{2} from both sides.

$$-xy+9x-9y=x^{2}+6x-27-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-xy+9x-9y=6x-27$$

Subtract 9x from both sides.

$$-xy-9y=6x-27-9x$$

Combine 6x and -9x to get -3x.

$$-xy-9y=-3x-27$$

Combine all terms containing y.

$$\left(-x-9\right)y=-3x-27$$

Divide both sides by -x-9.

$$\frac{\left(-x-9\right)y}{-x-9}=\frac{-3x-27}{-x-9}$$

Dividing by -x-9 undoes the multiplication by -x-9.

$$y=\frac{-3x-27}{-x-9}$$

Divide -3x-27 by -x-9.

$$y=3$$

Solve for x

$$\left\{\begin{matrix}\\x=-9\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+9 by x-y.

$$x^{2}+6x-27=x^{2}-xy+9x-9y$$

Subtract x^{2} from both sides.

$$x^{2}+6x-27-x^{2}=-xy+9x-9y$$

Combine x^{2} and -x^{2} to get 0.

$$6x-27=-xy+9x-9y$$

Add xy to both sides.

$$6x-27+xy=9x-9y$$

Subtract 9x from both sides.

$$6x-27+xy-9x=-9y$$

Combine 6x and -9x to get -3x.

$$-3x-27+xy=-9y$$

Add 27 to both sides.

$$-3x+xy=-9y+27$$

Combine all terms containing x.

$$\left(-3+y\right)x=-9y+27$$

The equation is in standard form.

$$\left(y-3\right)x=27-9y$$

Divide both sides by -3+y.

$$\frac{\left(y-3\right)x}{y-3}=\frac{27-9y}{y-3}$$

Dividing by -3+y undoes the multiplication by -3+y.

$$x=\frac{27-9y}{y-3}$$

Divide -9y+27 by -3+y.

$$x=-9$$

Solve for y

$$\left\{\begin{matrix}\\y=3\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=-9\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+9 by x-y.

$$x^{2}+6x-27=x^{2}-xy+9x-9y$$

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

$$x^{2}-xy+9x-9y=x^{2}+6x-27$$

Subtract x^{2} from both sides.

$$-xy+9x-9y=x^{2}+6x-27-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-xy+9x-9y=6x-27$$

Subtract 9x from both sides.

$$-xy-9y=6x-27-9x$$

Combine 6x and -9x to get -3x.

$$-xy-9y=-3x-27$$

Combine all terms containing y.

$$\left(-x-9\right)y=-3x-27$$

Divide both sides by -x-9.

$$\frac{\left(-x-9\right)y}{-x-9}=\frac{-3x-27}{-x-9}$$

Dividing by -x-9 undoes the multiplication by -x-9.

$$y=\frac{-3x-27}{-x-9}$$

Divide -3x-27 by -x-9.

$$y=3$$