3n(n2+1)=0

Divide each term in 3n(n2+1)=0 by 3.

3n(n2+1)3=03

Cancel the common factor.

3n(n2+1)3=03

Divide n(n2+1) by 1.

n(n2+1)=03

n(n2+1)=03

Divide 0 by 3.

n(n2+1)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

n=0

n2+1=0

Set the first factor equal to 0.

n=0

Set the next factor equal to 0.

n2+1=0

Subtract 1 from both sides of the equation.

n2=-1

Take the square root of both sides of the equation to eliminate the exponent on the left side.

n=±-1

The complete solution is the result of both the positive and negative portions of the solution.

Rewrite -1 as i.

n=±i

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

n=i

Next, use the negative value of the ± to find the second solution.

n=-i

The complete solution is the result of both the positive and negative portions of the solution.

n=i,-i

n=i,-i

n=i,-i

n=i,-i

The final solution is all the values that make 3n(n2+1)3=03 true.

n=0,i,-i

Solve for n 3n(n^2+1)=0