((x^2-2)*(x^2-2))-16(x^2-2)+28=0

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Solution for ((x^2-2)*(x^2-2))-16(x^2-2)+28=0 equation:


Simplifying
((x2 + -2)(x2 + -2)) + -16(x2 + -2) + 28 = 0

Reorder the terms:
((-2 + x2)(x2 + -2)) + -16(x2 + -2) + 28 = 0

Reorder the terms:
((-2 + x2)(-2 + x2)) + -16(x2 + -2) + 28 = 0

Multiply (-2 + x2) * (-2 + x2)
((-2(-2 + x2) + x2(-2 + x2))) + -16(x2 + -2) + 28 = 0
(((-2 * -2 + x2 * -2) + x2(-2 + x2))) + -16(x2 + -2) + 28 = 0
(((4 + -2x2) + x2(-2 + x2))) + -16(x2 + -2) + 28 = 0
((4 + -2x2 + (-2 * x2 + x2 * x2))) + -16(x2 + -2) + 28 = 0
((4 + -2x2 + (-2x2 + x4))) + -16(x2 + -2) + 28 = 0

Combine like terms: -2x2 + -2x2 = -4x2
((4 + -4x2 + x4)) + -16(x2 + -2) + 28 = 0
(4 + -4x2 + x4) + -16(x2 + -2) + 28 = 0

Remove parenthesis around (4 + -4x2 + x4)
4 + -4x2 + x4 + -16(x2 + -2) + 28 = 0

Reorder the terms:
4 + -4x2 + x4 + -16(-2 + x2) + 28 = 0
4 + -4x2 + x4 + (-2 * -16 + x2 * -16) + 28 = 0
4 + -4x2 + x4 + (32 + -16x2) + 28 = 0

Reorder the terms:
4 + 32 + 28 + -4x2 + -16x2 + x4 = 0

Combine like terms: 4 + 32 = 36
36 + 28 + -4x2 + -16x2 + x4 = 0

Combine like terms: 36 + 28 = 64
64 + -4x2 + -16x2 + x4 = 0

Combine like terms: -4x2 + -16x2 = -20x2
64 + -20x2 + x4 = 0

Solving
64 + -20x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(16 + -1x2) = 0

Factor a difference between two squares.
((4 + x)(4 + -1x))(2 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2, 2, -4, 4}

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