Solve x=x/-2t-4

$$x= \frac{ x }{ -2t-4 }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&t\neq -2\\x\in \mathrm{C}\text{, }&t=-\frac{5}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{x}{-2t-4} from both sides.

$$x-\frac{x}{-2t-4}=0$$

Factor -2t-4.

$$x-\frac{x}{2\left(-t-2\right)}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2\left(-t-2\right)}{2\left(-t-2\right)}.

$$\frac{x\times 2\left(-t-2\right)}{2\left(-t-2\right)}-\frac{x}{2\left(-t-2\right)}=0$$

Since \frac{x\times 2\left(-t-2\right)}{2\left(-t-2\right)} and \frac{x}{2\left(-t-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 2\left(-t-2\right)-x}{2\left(-t-2\right)}=0$$

Do the multiplications in x\times 2\left(-t-2\right)-x.

$$\frac{-2xt-4x-x}{2\left(-t-2\right)}=0$$

Combine like terms in -2xt-4x-x.

$$\frac{-2xt-5x}{2\left(-t-2\right)}=0$$

Multiply both sides of the equation by 2\left(-t-2\right).

$$-2xt-5x=0$$

Combine all terms containing x.

$$\left(-2t-5\right)x=0$$

Divide 0 by -2t-5.

$$x=0$$

Solve for t

$$\left\{\begin{matrix}\\t=-\frac{5}{2}=-2.5\text{, }&\text{unconditionally}\\t\neq -2\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable t cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 2\left(-t-2\right).

$$x\times 2\left(-t-2\right)=x$$

Use the distributive property to multiply x\times 2 by -t-2.

$$-2xt-2x\times 2=x$$

Multiply -2 and 2 to get -4.

$$-2xt-4x=x$$

Add 4x to both sides.

$$-2xt=x+4x$$

Combine x and 4x to get 5x.

$$-2xt=5x$$

The equation is in standard form.

$$\left(-2x\right)t=5x$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)t}{-2x}=\frac{5x}{-2x}$$

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

$$t=\frac{5x}{-2x}$$

Divide 5x by -2x.

$$t=-\frac{5}{2}$$

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&t\neq -2\\x\in \mathrm{R}\text{, }&t=-\frac{5}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{x}{-2t-4} from both sides.

$$x-\frac{x}{-2t-4}=0$$

Factor -2t-4.

$$x-\frac{x}{2\left(-t-2\right)}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2\left(-t-2\right)}{2\left(-t-2\right)}.

$$\frac{x\times 2\left(-t-2\right)}{2\left(-t-2\right)}-\frac{x}{2\left(-t-2\right)}=0$$

Since \frac{x\times 2\left(-t-2\right)}{2\left(-t-2\right)} and \frac{x}{2\left(-t-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 2\left(-t-2\right)-x}{2\left(-t-2\right)}=0$$

Do the multiplications in x\times 2\left(-t-2\right)-x.

$$\frac{-2xt-4x-x}{2\left(-t-2\right)}=0$$

Combine like terms in -2xt-4x-x.

$$\frac{-2xt-5x}{2\left(-t-2\right)}=0$$

Multiply both sides of the equation by 2\left(-t-2\right).

$$-2xt-5x=0$$

Combine all terms containing x.

$$\left(-2t-5\right)x=0$$

Divide 0 by -2t-5.

$$x=0$$