Solve (x+2)*(y-6)^2=81

$$( x + 2 ) \cdot ( y - 6 ) ^ { 2 } = 81$$

Solve for x

$$x=-\frac{2y^{2}-24y-9}{\left(y-6\right)^{2}}$$

$$y\neq 6$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-6\right)^{2}.

$$\left(x+2\right)\left(y^{2}-12y+36\right)=81$$

Use the distributive property to multiply x+2 by y^{2}-12y+36.

$$xy^{2}-12xy+36x+2y^{2}-24y+72=81$$

Subtract 2y^{2} from both sides.

$$xy^{2}-12xy+36x-24y+72=81-2y^{2}$$

Add 24y to both sides.

$$xy^{2}-12xy+36x+72=81-2y^{2}+24y$$

Subtract 72 from both sides.

$$xy^{2}-12xy+36x=81-2y^{2}+24y-72$$

Subtract 72 from 81 to get 9.

$$xy^{2}-12xy+36x=9-2y^{2}+24y$$

Combine all terms containing x.

$$\left(y^{2}-12y+36\right)x=9-2y^{2}+24y$$

The equation is in standard form.

$$\left(y^{2}-12y+36\right)x=9+24y-2y^{2}$$

Divide both sides by y^{2}-12y+36.

$$\frac{\left(y^{2}-12y+36\right)x}{y^{2}-12y+36}=\frac{9+24y-2y^{2}}{y^{2}-12y+36}$$

Dividing by y^{2}-12y+36 undoes the multiplication by y^{2}-12y+36.

$$x=\frac{9+24y-2y^{2}}{y^{2}-12y+36}$$

Divide 9-2y^{2}+24y by y^{2}-12y+36.

$$x=\frac{9+24y-2y^{2}}{\left(y-6\right)^{2}}$$

Solve for y (complex solution)

$$y=6+9\left(x+2\right)^{-\frac{1}{2}}$$

$$y=6-9\left(x+2\right)^{-\frac{1}{2}}\text{, }x\neq -2$$

Solve for y

$$y=6+\frac{9}{\sqrt{x+2}}$$

$$y=6-\frac{9}{\sqrt{x+2}}\text{, }x>-2$$