Solve 2x^2+(k-6)x-3k=0

$$2 x ^ { 2 } + ( k - 6 ) x - 3 k = 0$$

Solve for k (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply k-6 by x.

$$2x^{2}+kx-6x-3k=0$$

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

$$kx-6x-3k=-2x^{2}$$

Add 6x to both sides.

$$kx-3k=-2x^{2}+6x$$

Combine all terms containing k.

$$\left(x-3\right)k=-2x^{2}+6x$$

The equation is in standard form.

$$\left(x-3\right)k=6x-2x^{2}$$

Divide both sides by -3+x.

$$\frac{\left(x-3\right)k}{x-3}=\frac{2x\left(3-x\right)}{x-3}$$

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

$$k=\frac{2x\left(3-x\right)}{x-3}$$

Divide 2x\left(3-x\right) by -3+x.

$$k=-2x$$

Solve for k

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

Steps for Solving Linear Equation

Use the distributive property to multiply k-6 by x.

$$2x^{2}+kx-6x-3k=0$$

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

$$kx-6x-3k=-2x^{2}$$

Add 6x to both sides.

$$kx-3k=-2x^{2}+6x$$

Combine all terms containing k.

$$\left(x-3\right)k=-2x^{2}+6x$$

The equation is in standard form.

$$\left(x-3\right)k=6x-2x^{2}$$

Divide both sides by -3+x.

$$\frac{\left(x-3\right)k}{x-3}=\frac{2x\left(3-x\right)}{x-3}$$

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

$$k=\frac{2x\left(3-x\right)}{x-3}$$

Divide 2x\left(3-x\right) by -3+x.

$$k=-2x$$

Solve for x

$$x=-\frac{k}{2}$$

$$x=3$$