Solve 12(x+3)=(y+3)^2

$$12 ( x + 3 ) = ( y + 3 ) ^ { 2 }$$

Solve for x

$$x=-\frac{\left(3-y\right)\left(y+9\right)}{12}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 12 by x+3.

$$12x+36=\left(y+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+3\right)^{2}.

$$12x+36=y^{2}+6y+9$$

Subtract 36 from both sides.

$$12x=y^{2}+6y+9-36$$

Subtract 36 from 9 to get -27.

$$12x=y^{2}+6y-27$$

Divide both sides by 12.

$$\frac{12x}{12}=\frac{\left(y-3\right)\left(y+9\right)}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x=\frac{\left(y-3\right)\left(y+9\right)}{12}$$

Solve for y (complex solution)

$$y=-2\sqrt{3\left(x+3\right)}-3$$

$$y=2\sqrt{3\left(x+3\right)}-3$$

Solve for y

$$y=-2\sqrt{3\left(x+3\right)}-3$$

$$y=2\sqrt{3\left(x+3\right)}-3\text{, }x\geq -3$$