Solve 2x^2-12x+6m=0

$$2 x ^ { 2 } - 12 x + 6 m = 0$$

Solve for m

$$m=-\frac{x\left(x-6\right)}{3}$$

Steps for Solving Linear Equation

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

$$-12x+6m=-2x^{2}$$

Add 12x to both sides.

$$6m=-2x^{2}+12x$$

The equation is in standard form.

$$6m=12x-2x^{2}$$

Divide both sides by 6.

$$\frac{6m}{6}=\frac{2x\left(6-x\right)}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$m=\frac{2x\left(6-x\right)}{6}$$

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

$$m=\frac{x\left(6-x\right)}{3}$$

Solve for x (complex solution)

$$x=\sqrt{9-3m}+3$$

$$x=-\sqrt{9-3m}+3$$

Solve for x

$$x=\sqrt{9-3m}+3$$

$$x=-\sqrt{9-3m}+3\text{, }m\leq 3$$