Solve 3/n^2=n-4/3n^2+2/2n^2

$$\frac { 3 } { n ^ { 2 } } = \frac { n - 4 } { 3 n ^ { 2 } } + \frac { 2 } { 2 n ^ { 2 } }$$

Solve for n

$$n=10$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6n^{2}, the least common multiple of n^{2},3n^{2},2n^{2}.

$$6\times 3=2\left(n-4\right)+3\times 2$$

Multiply 6 and 3 to get 18.

$$18=2\left(n-4\right)+3\times 2$$

Use the distributive property to multiply 2 by n-4.

$$18=2n-8+3\times 2$$

Multiply 3 and 2 to get 6.

$$18=2n-8+6$$

Add -8 and 6 to get -2.

$$18=2n-2$$

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

$$2n-2=18$$

Add 2 to both sides.

$$2n=18+2$$

Add 18 and 2 to get 20.

$$2n=20$$

Divide both sides by 2.

$$n=\frac{20}{2}$$

Divide 20 by 2 to get 10.

$$n=10$$