Solve y=-ab-2by+2b^2=?

$$y = - a b - 2 b y + 2 b ^ { 2 } = ?$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$\left(-a\right)b-2by+2b^{2}=y$$

Add 2by to both sides.

$$\left(-a\right)b+2b^{2}=y+2by$$

Subtract 2b^{2} from both sides.

$$\left(-a\right)b=y+2by-2b^{2}$$

Reorder the terms.

$$-ab=2by+y-2b^{2}$$

The equation is in standard form.

$$\left(-b\right)a=2by+y-2b^{2}$$

Divide both sides by -b.

$$\frac{\left(-b\right)a}{-b}=\frac{2by+y-2b^{2}}{-b}$$

Dividing by -b undoes the multiplication by -b.

$$a=\frac{2by+y-2b^{2}}{-b}$$

Divide 2by+y-2b^{2} by -b.

$$a=2b-2y-\frac{y}{b}$$

Solve for a

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

Steps for Solving Linear Equation

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

$$\left(-a\right)b-2by+2b^{2}=y$$

Add 2by to both sides.

$$\left(-a\right)b+2b^{2}=y+2by$$

Subtract 2b^{2} from both sides.

$$\left(-a\right)b=y+2by-2b^{2}$$

Reorder the terms.

$$-ab=2by+y-2b^{2}$$

The equation is in standard form.

$$\left(-b\right)a=2by+y-2b^{2}$$

Divide both sides by -b.

$$\frac{\left(-b\right)a}{-b}=\frac{2by+y-2b^{2}}{-b}$$

Dividing by -b undoes the multiplication by -b.

$$a=\frac{2by+y-2b^{2}}{-b}$$

Divide 2by+y-2b^{2} by -b.

$$a=2b-2y-\frac{y}{b}$$

Solve for b (complex solution)

$$b=\frac{-\sqrt{4y^{2}+4ay+8y+a^{2}}+a+2y}{4}$$

$$b=\frac{\sqrt{4y^{2}+4ay+8y+a^{2}}+a+2y}{4}$$

Solve for b

$$b=\frac{-\sqrt{4y^{2}+4ay+8y+a^{2}}+a+2y}{4}$$

$$b=\frac{\sqrt{4y^{2}+4ay+8y+a^{2}}+a+2y}{4}\text{, }y\geq -\frac{a}{2}+\sqrt{a+1}-1\text{ or }y\leq -\frac{a}{2}-\sqrt{a+1}-1\text{ or }a\leq -1$$