Solve 6x^2+(12-8a)x-16a=0

$$6 x ^ { 2 } + ( 12 - 8 a ) x - 16 a = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=\frac{3x}{4}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 12-8a by x.

$$6x^{2}+12x-8ax-16a=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$12x-8ax-16a=-6x^{2}$$

Subtract 12x from both sides.

$$-8ax-16a=-6x^{2}-12x$$

Combine all terms containing a.

$$\left(-8x-16\right)a=-6x^{2}-12x$$

Divide both sides by -8x-16.

$$\frac{\left(-8x-16\right)a}{-8x-16}=-\frac{6x\left(x+2\right)}{-8x-16}$$

Dividing by -8x-16 undoes the multiplication by -8x-16.

$$a=-\frac{6x\left(x+2\right)}{-8x-16}$$

Divide -6x\left(2+x\right) by -8x-16.

$$a=\frac{3x}{4}$$

Solve for a

$$\left\{\begin{matrix}\\a=\frac{3x}{4}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 12-8a by x.

$$6x^{2}+12x-8ax-16a=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$12x-8ax-16a=-6x^{2}$$

Subtract 12x from both sides.

$$-8ax-16a=-6x^{2}-12x$$

Combine all terms containing a.

$$\left(-8x-16\right)a=-6x^{2}-12x$$

Divide both sides by -8x-16.

$$\frac{\left(-8x-16\right)a}{-8x-16}=-\frac{6x\left(x+2\right)}{-8x-16}$$

Dividing by -8x-16 undoes the multiplication by -8x-16.

$$a=-\frac{6x\left(x+2\right)}{-8x-16}$$

Divide -6x\left(2+x\right) by -8x-16.

$$a=\frac{3x}{4}$$

Solve for x

$$x=\frac{4a}{3}$$

$$x=-2$$