Solve n=sqrt{6n}

$$n = \sqrt { 6 n }$$

Solve for n

$$n=6$$

$$n=0$$

Solution Steps

Square both sides of the equation.

$$n^{2}=\left(\sqrt{6n}\right)^{2}$$

Calculate \sqrt{6n} to the power of 2 and get 6n.

$$n^{2}=6n$$

Subtract 6n from both sides.

$$n^{2}-6n=0$$

Factor out n.

$$n\left(n-6\right)=0$$

To find equation solutions, solve n=0 and n-6=0.

$$n=0 n=6$$

Substitute 0 for n in the equation n=\sqrt{6n}.

$$0=\sqrt{6\times 0}$$

Simplify. The value n=0 satisfies the equation.

$$0=0$$

Substitute 6 for n in the equation n=\sqrt{6n}.

$$6=\sqrt{6\times 6}$$

Simplify. The value n=6 satisfies the equation.

$$6=6$$

List all solutions of n=\sqrt{6n}.

$$n=0 n=6$$