(y+2)(y-2)(y^2+4)=0

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Solution for (y+2)(y-2)(y^2+4)=0 equation: 


Simplifying
(y + 2)(y + -2)(y2 + 4) = 0

Reorder the terms:
(2 + y)(y + -2)(y2 + 4) = 0

Reorder the terms:
(2 + y)(-2 + y)(y2 + 4) = 0

Reorder the terms:
(2 + y)(-2 + y)(4 + y2) = 0

Multiply (2 + y) * (-2 + y)
(2(-2 + y) + y(-2 + y))(4 + y2) = 0
((-2 * 2 + y * 2) + y(-2 + y))(4 + y2) = 0
((-4 + 2y) + y(-2 + y))(4 + y2) = 0
(-4 + 2y + (-2 * y + y * y))(4 + y2) = 0
(-4 + 2y + (-2y + y2))(4 + y2) = 0

Combine like terms: 2y + -2y = 0
(-4 + 0 + y2)(4 + y2) = 0
(-4 + y2)(4 + y2) = 0

Multiply (-4 + y2) * (4 + y2)
(-4(4 + y2) + y2(4 + y2)) = 0
((4 * -4 + y2 * -4) + y2(4 + y2)) = 0
((-16 + -4y2) + y2(4 + y2)) = 0
(-16 + -4y2 + (4 * y2 + y2 * y2)) = 0
(-16 + -4y2 + (4y2 + y4)) = 0

Combine like terms: -4y2 + 4y2 = 0
(-16 + 0 + y4) = 0
(-16 + y4) = 0

Solving
-16 + y4 = 0

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '16' to each side of the equation.
-16 + 16 + y4 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + y4 = 0 + 16
y4 = 0 + 16

Combine like terms: 0 + 16 = 16
y4 = 16

Simplifying
y4 = 16

Reorder the terms:
-16 + y4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + y4 = 0

Factor a difference between two squares.
(4 + y2)(-4 + y2) = 0

Factor a difference between two squares.
(4 + y2)((2 + y)(-2 + y)) = 0


Subproblem 1
Set the factor '(4 + y2)' equal to zero and attempt to solve:

Simplifying
4 + y2 = 0

Solving
4 + y2 = 0

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y2 = 0 + -4
y2 = 0 + -4

Combine like terms: 0 + -4 = -4
y2 = -4

Simplifying
y2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2

Subproblem 3
Set the factor '(-2 + y)' equal to zero and attempt to solve:

Simplifying
-2 + y = 0

Solving
-2 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + y = 0 + 2
y = 0 + 2

Combine like terms: 0 + 2 = 2
y = 2

Simplifying
y = 2
Solution
y = {-2, 2}

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