Solve x^2+ax+2a-4=0

$$x ^ { 2 } + a x + 2 a - 4 = 0$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$ax+2a-4=-x^{2}$$

Add 4 to both sides.

$$ax+2a=-x^{2}+4$$

Combine all terms containing a.

$$\left(x+2\right)a=-x^{2}+4$$

The equation is in standard form.

$$\left(x+2\right)a=4-x^{2}$$

Divide both sides by 2+x.

$$\frac{\left(x+2\right)a}{x+2}=\frac{4-x^{2}}{x+2}$$

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

$$a=\frac{4-x^{2}}{x+2}$$

Divide -x^{2}+4 by 2+x.

$$a=2-x$$

Solve for a

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$ax+2a-4=-x^{2}$$

Add 4 to both sides.

$$ax+2a=-x^{2}+4$$

Combine all terms containing a.

$$\left(x+2\right)a=-x^{2}+4$$

The equation is in standard form.

$$\left(x+2\right)a=4-x^{2}$$

Divide both sides by 2+x.

$$\frac{\left(x+2\right)a}{x+2}=\frac{4-x^{2}}{x+2}$$

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

$$a=\frac{4-x^{2}}{x+2}$$

Divide -x^{2}+4 by 2+x.

$$a=2-x$$

Solve for x

$$x=-2$$

$$x=2-a$$