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

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

Solve for m

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

Steps for Solving Linear Equation

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

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

Add 12a to both sides.

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

The equation is in standard form.

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

Divide both sides by 6.

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

Dividing by 6 undoes the multiplication by 6.

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

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

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

Solve for a

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

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