Solve -2y(x-4)=0

$$-2y(x-4)=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=4\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2y by x-4.

$$-2yx+8y=0$$

Subtract 8y from both sides. Anything subtracted from zero gives its negation.

$$-2yx=-8y$$

The equation is in standard form.

$$\left(-2y\right)x=-8y$$

Divide both sides by -2y.

$$\frac{\left(-2y\right)x}{-2y}=-\frac{8y}{-2y}$$

Dividing by -2y undoes the multiplication by -2y.

$$x=-\frac{8y}{-2y}$$

Divide -8y by -2y.

$$x=4$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2y by x-4.

$$-2yx+8y=0$$

Combine all terms containing y.

$$\left(-2x+8\right)y=0$$

The equation is in standard form.

$$\left(8-2x\right)y=0$$

Divide 0 by -2x+8.

$$y=0$$

Solve for x

$$\left\{\begin{matrix}\\x=4\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2y by x-4.

$$-2yx+8y=0$$

Subtract 8y from both sides. Anything subtracted from zero gives its negation.

$$-2yx=-8y$$

The equation is in standard form.

$$\left(-2y\right)x=-8y$$

Divide both sides by -2y.

$$\frac{\left(-2y\right)x}{-2y}=-\frac{8y}{-2y}$$

Dividing by -2y undoes the multiplication by -2y.

$$x=-\frac{8y}{-2y}$$

Divide -8y by -2y.

$$x=4$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2y by x-4.

$$-2yx+8y=0$$

Combine all terms containing y.

$$\left(-2x+8\right)y=0$$

The equation is in standard form.

$$\left(8-2x\right)y=0$$

Divide 0 by -2x+8.

$$y=0$$