Solve -5x(2y+4)-y=2

$$- 5 x ( 2 y + 4 ) - y = 2$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\frac{1}{10}=-0.1\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5x by 2y+4.

$$-10xy-20x-y=2$$

Add y to both sides.

$$-10xy-20x=2+y$$

Combine all terms containing x.

$$\left(-10y-20\right)x=2+y$$

The equation is in standard form.

$$\left(-10y-20\right)x=y+2$$

Divide both sides by -10y-20.

$$\frac{\left(-10y-20\right)x}{-10y-20}=\frac{y+2}{-10y-20}$$

Dividing by -10y-20 undoes the multiplication by -10y-20.

$$x=\frac{y+2}{-10y-20}$$

Divide 2+y by -10y-20.

$$x=-\frac{1}{10}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=-2\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=-\frac{1}{10}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5x by 2y+4.

$$-10xy-20x-y=2$$

Add 20x to both sides.

$$-10xy-y=2+20x$$

Combine all terms containing y.

$$\left(-10x-1\right)y=2+20x$$

The equation is in standard form.

$$\left(-10x-1\right)y=20x+2$$

Divide both sides by -1-10x.

$$\frac{\left(-10x-1\right)y}{-10x-1}=\frac{20x+2}{-10x-1}$$

Dividing by -1-10x undoes the multiplication by -1-10x.

$$y=\frac{20x+2}{-10x-1}$$

Divide 2+20x by -1-10x.

$$y=-2$$

Solve for x

$$\left\{\begin{matrix}\\x=-\frac{1}{10}=-0.1\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5x by 2y+4.

$$-10xy-20x-y=2$$

Add y to both sides.

$$-10xy-20x=2+y$$

Combine all terms containing x.

$$\left(-10y-20\right)x=2+y$$

The equation is in standard form.

$$\left(-10y-20\right)x=y+2$$

Divide both sides by -10y-20.

$$\frac{\left(-10y-20\right)x}{-10y-20}=\frac{y+2}{-10y-20}$$

Dividing by -10y-20 undoes the multiplication by -10y-20.

$$x=\frac{y+2}{-10y-20}$$

Divide 2+y by -10y-20.

$$x=-\frac{1}{10}$$

Solve for y

$$\left\{\begin{matrix}\\y=-2\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=-\frac{1}{10}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5x by 2y+4.

$$-10xy-20x-y=2$$

Add 20x to both sides.

$$-10xy-y=2+20x$$

Combine all terms containing y.

$$\left(-10x-1\right)y=2+20x$$

The equation is in standard form.

$$\left(-10x-1\right)y=20x+2$$

Divide both sides by -1-10x.

$$\frac{\left(-10x-1\right)y}{-10x-1}=\frac{20x+2}{-10x-1}$$

Dividing by -1-10x undoes the multiplication by -1-10x.

$$y=\frac{20x+2}{-10x-1}$$

Divide 2+20x by -1-10x.

$$y=-2$$