Solve x^2+6x-27={(x+9)}{(x-a)}

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$x^{2}+6x-27=x^{2}-xa+9x-9a$$

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

$$x^{2}-xa+9x-9a=x^{2}+6x-27$$

Subtract x^{2} from both sides.

$$-xa+9x-9a=x^{2}+6x-27-x^{2}$$

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

$$-xa+9x-9a=6x-27$$

Subtract 9x from both sides.

$$-xa-9a=6x-27-9x$$

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

$$-xa-9a=-3x-27$$

Combine all terms containing a.

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

Divide both sides by -x-9.

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

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

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

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

$$a=3$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$x^{2}+6x-27=x^{2}-xa+9x-9a$$

Subtract x^{2} from both sides.

$$x^{2}+6x-27-x^{2}=-xa+9x-9a$$

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

$$6x-27=-xa+9x-9a$$

Add xa to both sides.

$$6x-27+xa=9x-9a$$

Subtract 9x from both sides.

$$6x-27+xa-9x=-9a$$

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

$$-3x-27+xa=-9a$$

Add 27 to both sides.

$$-3x+xa=-9a+27$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -3+a.

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

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

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

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

$$x=-9$$

Solve for a

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

Steps for Solving Linear Equation

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

$$x^{2}+6x-27=x^{2}-xa+9x-9a$$

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

$$x^{2}-xa+9x-9a=x^{2}+6x-27$$

Subtract x^{2} from both sides.

$$-xa+9x-9a=x^{2}+6x-27-x^{2}$$

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

$$-xa+9x-9a=6x-27$$

Subtract 9x from both sides.

$$-xa-9a=6x-27-9x$$

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

$$-xa-9a=-3x-27$$

Combine all terms containing a.

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

Divide both sides by -x-9.

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

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

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

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

$$a=3$$

Solve for x

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

Steps for Solving Linear Equation

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

$$x^{2}+6x-27=x^{2}-xa+9x-9a$$

Subtract x^{2} from both sides.

$$x^{2}+6x-27-x^{2}=-xa+9x-9a$$

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

$$6x-27=-xa+9x-9a$$

Add xa to both sides.

$$6x-27+xa=9x-9a$$

Subtract 9x from both sides.

$$6x-27+xa-9x=-9a$$

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

$$-3x-27+xa=-9a$$

Add 27 to both sides.

$$-3x+xa=-9a+27$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -3+a.

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

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

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

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

$$x=-9$$