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

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


Simplifying
(x2 + 4x + 4)(x2 + -4x + 4) = 0

Reorder the terms:
(4 + 4x + x2)(x2 + -4x + 4) = 0

Reorder the terms:
(4 + 4x + x2)(4 + -4x + x2) = 0

Multiply (4 + 4x + x2) * (4 + -4x + x2)
(4(4 + -4x + x2) + 4x * (4 + -4x + x2) + x2(4 + -4x + x2)) = 0
((4 * 4 + -4x * 4 + x2 * 4) + 4x * (4 + -4x + x2) + x2(4 + -4x + x2)) = 0
((16 + -16x + 4x2) + 4x * (4 + -4x + x2) + x2(4 + -4x + x2)) = 0
(16 + -16x + 4x2 + (4 * 4x + -4x * 4x + x2 * 4x) + x2(4 + -4x + x2)) = 0
(16 + -16x + 4x2 + (16x + -16x2 + 4x3) + x2(4 + -4x + x2)) = 0
(16 + -16x + 4x2 + 16x + -16x2 + 4x3 + (4 * x2 + -4x * x2 + x2 * x2)) = 0
(16 + -16x + 4x2 + 16x + -16x2 + 4x3 + (4x2 + -4x3 + x4)) = 0

Reorder the terms:
(16 + -16x + 16x + 4x2 + -16x2 + 4x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: -16x + 16x = 0
(16 + 0 + 4x2 + -16x2 + 4x2 + 4x3 + -4x3 + x4) = 0
(16 + 4x2 + -16x2 + 4x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: 4x2 + -16x2 = -12x2
(16 + -12x2 + 4x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: -12x2 + 4x2 = -8x2
(16 + -8x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: 4x3 + -4x3 = 0
(16 + -8x2 + 0 + x4) = 0
(16 + -8x2 + x4) = 0

Solving
16 + -8x2 + x4 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
((2 + x)(2 + -1x))(4 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -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 '(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 4

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

Solution

x = {-2, 2, -2, 2}

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