Solve -3/n=2n/-6

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

Solve for n

$$n=3$$

$$n=-3$$

Steps by Finding Square Root

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6n, the least common multiple of n,-6.

$$6\left(-3\right)=-n\times 2n$$

Multiply 6 and -3 to get -18.

$$-18=-n\times 2n$$

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

$$-18=-n^{2}\times 2$$

Multiply -1 and 2 to get -2.

$$-18=-2n^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-2n^{2}=-18$$

Divide both sides by -2.

$$n^{2}=\frac{-18}{-2}$$

Divide -18 by -2 to get 9.

$$n^{2}=9$$

Take the square root of both sides of the equation.

$$n=3 n=-3$$

Steps Using the Quadratic Formula

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6n, the least common multiple of n,-6.

$$6\left(-3\right)=-n\times 2n$$

Multiply 6 and -3 to get -18.

$$-18=-n\times 2n$$

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

$$-18=-n^{2}\times 2$$

Multiply -1 and 2 to get -2.

$$-18=-2n^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-2n^{2}=-18$$

Add 18 to both sides.

$$-2n^{2}+18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 18}}{2\left(-2\right)}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-2\right)\times 18}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$n=\frac{0±\sqrt{8\times 18}}{2\left(-2\right)}$$

Multiply 8 times 18.

$$n=\frac{0±\sqrt{144}}{2\left(-2\right)}$$

Take the square root of 144.

$$n=\frac{0±12}{2\left(-2\right)}$$

Multiply 2 times -2.

$$n=\frac{0±12}{-4}$$

Now solve the equation n=\frac{0±12}{-4} when ± is plus. Divide 12 by -4.

$$n=-3$$

Now solve the equation n=\frac{0±12}{-4} when ± is minus. Divide -12 by -4.

$$n=3$$

The equation is now solved.

$$n=-3 n=3$$