Solve -3n^2+6n/3n=2-n

$$\frac { - 3 n ^ { 2 } + 6 n } { 3 n } = 2 - n$$

Solve for n

$$n\neq 0$$

Solution Steps

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3n.

$$-3n^{2}+6n=3n\times 2-n\times 3n$$

Multiply n and n to get n^{2}.

$$-3n^{2}+6n=3n\times 2-n^{2}\times 3$$

Multiply 3 and 2 to get 6.

$$-3n^{2}+6n=6n-n^{2}\times 3$$

Multiply -1 and 3 to get -3.

$$-3n^{2}+6n=6n-3n^{2}$$

Subtract 6n from both sides.

$$-3n^{2}+6n-6n=-3n^{2}$$

Combine 6n and -6n to get 0.

$$-3n^{2}=-3n^{2}$$

Add 3n^{2} to both sides.

$$-3n^{2}+3n^{2}=0$$

Combine -3n^{2} and 3n^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any n.

$$n\in \mathrm{R}$$

Variable n cannot be equal to 0.

$$n\in \mathrm{R}\setminus 0$$