Solve y=xy(y-5)+5(2xy+6xy)

$$y = x y ( y - 5 ) + 5 ( 2 x y + 6 x y )$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{1}{y+35}\text{, }&y\neq -35\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply xy by y-5.

$$y=xy^{2}-5xy+5\left(2xy+6xy\right)$$

Combine 2xy and 6xy to get 8xy.

$$y=xy^{2}-5xy+5\times 8xy$$

Multiply 5 and 8 to get 40.

$$y=xy^{2}-5xy+40xy$$

Combine -5xy and 40xy to get 35xy.

$$y=xy^{2}+35xy$$

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

$$xy^{2}+35xy=y$$

Combine all terms containing x.

$$\left(y^{2}+35y\right)x=y$$

Divide both sides by y^{2}+35y.

$$\frac{\left(y^{2}+35y\right)x}{y^{2}+35y}=\frac{y}{y^{2}+35y}$$

Dividing by y^{2}+35y undoes the multiplication by y^{2}+35y.

$$x=\frac{y}{y^{2}+35y}$$

Divide y by y^{2}+35y.

$$x=\frac{1}{y+35}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{1}{y+35}\text{, }&y\neq -35\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply xy by y-5.

$$y=xy^{2}-5xy+5\left(2xy+6xy\right)$$

Combine 2xy and 6xy to get 8xy.

$$y=xy^{2}-5xy+5\times 8xy$$

Multiply 5 and 8 to get 40.

$$y=xy^{2}-5xy+40xy$$

Combine -5xy and 40xy to get 35xy.

$$y=xy^{2}+35xy$$

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

$$xy^{2}+35xy=y$$

Combine all terms containing x.

$$\left(y^{2}+35y\right)x=y$$

Divide both sides by y^{2}+35y.

$$\frac{\left(y^{2}+35y\right)x}{y^{2}+35y}=\frac{y}{y^{2}+35y}$$

Dividing by y^{2}+35y undoes the multiplication by y^{2}+35y.

$$x=\frac{y}{y^{2}+35y}$$

Divide y by y^{2}+35y.

$$x=\frac{1}{y+35}$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=-35+\frac{1}{x}\text{, }&x\neq 0\end{matrix}\right.$$