Solve x^2+(3a-4)x-12a=0

$$x ^ { 2 } + ( 3 a - 4 ) x - 12 a = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=-\frac{x}{3}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3a-4 by x.

$$x^{2}+3ax-4x-12a=0$$

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

$$3ax-4x-12a=-x^{2}$$

Add 4x to both sides.

$$3ax-12a=-x^{2}+4x$$

Combine all terms containing a.

$$\left(3x-12\right)a=-x^{2}+4x$$

The equation is in standard form.

$$\left(3x-12\right)a=4x-x^{2}$$

Divide both sides by 3x-12.

$$\frac{\left(3x-12\right)a}{3x-12}=\frac{x\left(4-x\right)}{3x-12}$$

Dividing by 3x-12 undoes the multiplication by 3x-12.

$$a=\frac{x\left(4-x\right)}{3x-12}$$

Divide x\left(4-x\right) by 3x-12.

$$a=-\frac{x}{3}$$

Solve for a

$$\left\{\begin{matrix}\\a=-\frac{x}{3}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3a-4 by x.

$$x^{2}+3ax-4x-12a=0$$

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

$$3ax-4x-12a=-x^{2}$$

Add 4x to both sides.

$$3ax-12a=-x^{2}+4x$$

Combine all terms containing a.

$$\left(3x-12\right)a=-x^{2}+4x$$

The equation is in standard form.

$$\left(3x-12\right)a=4x-x^{2}$$

Divide both sides by 3x-12.

$$\frac{\left(3x-12\right)a}{3x-12}=\frac{x\left(4-x\right)}{3x-12}$$

Dividing by 3x-12 undoes the multiplication by 3x-12.

$$a=\frac{x\left(4-x\right)}{3x-12}$$

Divide x\left(4-x\right) by 3x-12.

$$a=-\frac{x}{3}$$

Solve for x

$$x=-3a$$

$$x=4$$