Solve (x+9y)*b=x^2+2xy+27y^2

$$( x + 9 y ) \times b = x ^ { 2 } + 2 x y + 27 y ^ { 2 }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{x^{2}+2xy+27y^{2}}{x+9y}\text{, }&x\neq -9y\\b\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide both sides by x+9y.

$$\frac{\left(x+9y\right)b}{x+9y}=\frac{x^{2}+2xy+27y^{2}}{x+9y}$$

Dividing by x+9y undoes the multiplication by x+9y.

$$b=\frac{x^{2}+2xy+27y^{2}}{x+9y}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{x^{2}+2xy+27y^{2}}{x+9y}\text{, }&x\neq -9y\\b\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide both sides by x+9y.

$$\frac{\left(x+9y\right)b}{x+9y}=\frac{x^{2}+2xy+27y^{2}}{x+9y}$$

Dividing by x+9y undoes the multiplication by x+9y.

$$b=\frac{x^{2}+2xy+27y^{2}}{x+9y}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{b^{2}+32by-104y^{2}}+b-2y}{2}$$

$$x=\frac{\sqrt{b^{2}+32by-104y^{2}}+b-2y}{2}$$

Solve for x

$$x=\frac{-\sqrt{b^{2}+32by-104y^{2}}+b-2y}{2}$$

$$x=\frac{\sqrt{b^{2}+32by-104y^{2}}+b-2y}{2}\text{, }y\geq -\frac{3\sqrt{10}|b|}{52}+\frac{2b}{13}\text{ and }y\leq \frac{3\sqrt{10}|b|}{52}+\frac{2b}{13}$$