y5+16y=0

Factor y out of y5.

y⋅y4+16y=0

Factor y out of 16y.

y⋅y4+y⋅16=0

Factor y out of y⋅y4+y⋅16.

y(y4+16)=0

y(y4+16)=0

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

y=0

y4+16=0

Set the first factor equal to 0.

y=0

Set the next factor equal to 0.

y4+16=0

Subtract 16 from both sides of the equation.

y4=-16

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

y=±-164

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

Simplify the right side of the equation.

Rewrite -16 as 24⋅-1.

Factor 16 out of -16.

y=±16(-1)4

Rewrite 16 as 24.

y=±24⋅-14

y=±24⋅-14

Pull terms out from under the radical.

y=±2-14

y=±2-14

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.

y=2-14

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

y=-2-14

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

y=2-14,-2-14

y=2-14,-2-14

y=2-14,-2-14

y=2-14,-2-14

The final solution is all the values that make y(y4+16)=0 true.

y=0,2-14,-2-14

Solve for y y^5+16y=0