Solve ax+2a(a+3)=2y

$$a x + 2 a ( a + 3 ) = 2 y$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-2a+\frac{2y}{a}-6\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2a by a+3.

$$ax+2a^{2}+6a=2y$$

Subtract 2a^{2} from both sides.

$$ax+6a=2y-2a^{2}$$

Subtract 6a from both sides.

$$ax=2y-2a^{2}-6a$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{2y-2a^{2}-6a}{a}$$

Dividing by a undoes the multiplication by a.

$$x=\frac{2y-2a^{2}-6a}{a}$$

Divide 2y-2a^{2}-6a by a.

$$x=-2a+\frac{2y}{a}-6$$

Solve for x

$$\left\{\begin{matrix}x=-2a+\frac{2y}{a}-6\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2a by a+3.

$$ax+2a^{2}+6a=2y$$

Subtract 2a^{2} from both sides.

$$ax+6a=2y-2a^{2}$$

Subtract 6a from both sides.

$$ax=2y-2a^{2}-6a$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{2y-2a^{2}-6a}{a}$$

Dividing by a undoes the multiplication by a.

$$x=\frac{2y-2a^{2}-6a}{a}$$

Divide 2y-2a^{2}-6a by a.

$$x=-2a+\frac{2y}{a}-6$$

Solve for a (complex solution)

$$a=\frac{\sqrt{x^{2}+12x+16y+36}}{4}-\frac{x}{4}-\frac{3}{2}$$

$$a=-\frac{\sqrt{x^{2}+12x+16y+36}}{4}-\frac{x}{4}-\frac{3}{2}$$

Solve for a

$$a=\frac{\sqrt{x^{2}+12x+16y+36}}{4}-\frac{x}{4}-\frac{3}{2}$$

$$a=-\frac{\sqrt{x^{2}+12x+16y+36}}{4}-\frac{x}{4}-\frac{3}{2}\text{, }y\geq -\frac{\left(x+6\right)^{2}}{16}$$