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

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


Simplifying
(x + 4)(x + -4)(x + -2)(x + 2) = (x + 4)(x + -4)(x + 2)(x + -2)

Reorder the terms:
(4 + x)(x + -4)(x + -2)(x + 2) = (x + 4)(x + -4)(x + 2)(x + -2)

Reorder the terms:
(4 + x)(-4 + x)(x + -2)(x + 2) = (x + 4)(x + -4)(x + 2)(x + -2)

Reorder the terms:
(4 + x)(-4 + x)(-2 + x)(x + 2) = (x + 4)(x + -4)(x + 2)(x + -2)

Reorder the terms:
(4 + x)(-4 + x)(-2 + x)(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)

Multiply (4 + x) * (-4 + x)
(4(-4 + x) + x(-4 + x))(-2 + x)(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
((-4 * 4 + x * 4) + x(-4 + x))(-2 + x)(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
((-16 + 4x) + x(-4 + x))(-2 + x)(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
(-16 + 4x + (-4 * x + x * x))(-2 + x)(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
(-16 + 4x + (-4x + x2))(-2 + x)(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)

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

Multiply (-16 + x2) * (-2 + x)
(-16(-2 + x) + x2(-2 + x))(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
((-2 * -16 + x * -16) + x2(-2 + x))(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
((32 + -16x) + x2(-2 + x))(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
(32 + -16x + (-2 * x2 + x * x2))(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
(32 + -16x + (-2x2 + x3))(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)
(32 + -16x + -2x2 + x3)(2 + x) = (x + 4)(x + -4)(x + 2)(x + -2)

Multiply (32 + -16x + -2x2 + x3) * (2 + x)
(32(2 + x) + -16x * (2 + x) + -2x2 * (2 + x) + x3(2 + x)) = (x + 4)(x + -4)(x + 2)(x + -2)
((2 * 32 + x * 32) + -16x * (2 + x) + -2x2 * (2 + x) + x3(2 + x)) = (x + 4)(x + -4)(x + 2)(x + -2)
((64 + 32x) + -16x * (2 + x) + -2x2 * (2 + x) + x3(2 + x)) = (x + 4)(x + -4)(x + 2)(x + -2)
(64 + 32x + (2 * -16x + x * -16x) + -2x2 * (2 + x) + x3(2 + x)) = (x + 4)(x + -4)(x + 2)(x + -2)
(64 + 32x + (-32x + -16x2) + -2x2 * (2 + x) + x3(2 + x)) = (x + 4)(x + -4)(x + 2)(x + -2)
(64 + 32x + -32x + -16x2 + (2 * -2x2 + x * -2x2) + x3(2 + x)) = (x + 4)(x + -4)(x + 2)(x + -2)
(64 + 32x + -32x + -16x2 + (-4x2 + -2x3) + x3(2 + x)) = (x + 4)(x + -4)(x + 2)(x + -2)
(64 + 32x + -32x + -16x2 + -4x2 + -2x3 + (2 * x3 + x * x3)) = (x + 4)(x + -4)(x + 2)(x + -2)
(64 + 32x + -32x + -16x2 + -4x2 + -2x3 + (2x3 + x4)) = (x + 4)(x + -4)(x + 2)(x + -2)

Combine like terms: 32x + -32x = 0
(64 + 0 + -16x2 + -4x2 + -2x3 + 2x3 + x4) = (x + 4)(x + -4)(x + 2)(x + -2)
(64 + -16x2 + -4x2 + -2x3 + 2x3 + x4) = (x + 4)(x + -4)(x + 2)(x + -2)

Combine like terms: -16x2 + -4x2 = -20x2
(64 + -20x2 + -2x3 + 2x3 + x4) = (x + 4)(x + -4)(x + 2)(x + -2)

Combine like terms: -2x3 + 2x3 = 0
(64 + -20x2 + 0 + x4) = (x + 4)(x + -4)(x + 2)(x + -2)
(64 + -20x2 + x4) = (x + 4)(x + -4)(x + 2)(x + -2)

Reorder the terms:
64 + -20x2 + x4 = (4 + x)(x + -4)(x + 2)(x + -2)

Reorder the terms:
64 + -20x2 + x4 = (4 + x)(-4 + x)(x + 2)(x + -2)

Reorder the terms:
64 + -20x2 + x4 = (4 + x)(-4 + x)(2 + x)(x + -2)

Reorder the terms:
64 + -20x2 + x4 = (4 + x)(-4 + x)(2 + x)(-2 + x)

Multiply (4 + x) * (-4 + x)
64 + -20x2 + x4 = (4(-4 + x) + x(-4 + x))(2 + x)(-2 + x)
64 + -20x2 + x4 = ((-4 * 4 + x * 4) + x(-4 + x))(2 + x)(-2 + x)
64 + -20x2 + x4 = ((-16 + 4x) + x(-4 + x))(2 + x)(-2 + x)
64 + -20x2 + x4 = (-16 + 4x + (-4 * x + x * x))(2 + x)(-2 + x)
64 + -20x2 + x4 = (-16 + 4x + (-4x + x2))(2 + x)(-2 + x)

Combine like terms: 4x + -4x = 0
64 + -20x2 + x4 = (-16 + 0 + x2)(2 + x)(-2 + x)
64 + -20x2 + x4 = (-16 + x2)(2 + x)(-2 + x)

Multiply (-16 + x2) * (2 + x)
64 + -20x2 + x4 = (-16(2 + x) + x2(2 + x))(-2 + x)
64 + -20x2 + x4 = ((2 * -16 + x * -16) + x2(2 + x))(-2 + x)
64 + -20x2 + x4 = ((-32 + -16x) + x2(2 + x))(-2 + x)
64 + -20x2 + x4 = (-32 + -16x + (2 * x2 + x * x2))(-2 + x)
64 + -20x2 + x4 = (-32 + -16x + (2x2 + x3))(-2 + x)
64 + -20x2 + x4 = (-32 + -16x + 2x2 + x3)(-2 + x)

Multiply (-32 + -16x + 2x2 + x3) * (-2 + x)
64 + -20x2 + x4 = (-32(-2 + x) + -16x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x))
64 + -20x2 + x4 = ((-2 * -32 + x * -32) + -16x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x))
64 + -20x2 + x4 = ((64 + -32x) + -16x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x))
64 + -20x2 + x4 = (64 + -32x + (-2 * -16x + x * -16x) + 2x2 * (-2 + x) + x3(-2 + x))
64 + -20x2 + x4 = (64 + -32x + (32x + -16x2) + 2x2 * (-2 + x) + x3(-2 + x))
64 + -20x2 + x4 = (64 + -32x + 32x + -16x2 + (-2 * 2x2 + x * 2x2) + x3(-2 + x))
64 + -20x2 + x4 = (64 + -32x + 32x + -16x2 + (-4x2 + 2x3) + x3(-2 + x))
64 + -20x2 + x4 = (64 + -32x + 32x + -16x2 + -4x2 + 2x3 + (-2 * x3 + x * x3))
64 + -20x2 + x4 = (64 + -32x + 32x + -16x2 + -4x2 + 2x3 + (-2x3 + x4))

Combine like terms: -32x + 32x = 0
64 + -20x2 + x4 = (64 + 0 + -16x2 + -4x2 + 2x3 + -2x3 + x4)
64 + -20x2 + x4 = (64 + -16x2 + -4x2 + 2x3 + -2x3 + x4)

Combine like terms: -16x2 + -4x2 = -20x2
64 + -20x2 + x4 = (64 + -20x2 + 2x3 + -2x3 + x4)

Combine like terms: 2x3 + -2x3 = 0
64 + -20x2 + x4 = (64 + -20x2 + 0 + x4)
64 + -20x2 + x4 = (64 + -20x2 + x4)

Add '-64' to each side of the equation.
64 + -20x2 + -64 + x4 = 64 + -20x2 + -64 + x4

Reorder the terms:
64 + -64 + -20x2 + x4 = 64 + -20x2 + -64 + x4

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

Reorder the terms:
-20x2 + x4 = 64 + -64 + -20x2 + x4

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

Add '20x2' to each side of the equation.
-20x2 + 20x2 + x4 = -20x2 + 20x2 + x4

Combine like terms: -20x2 + 20x2 = 0
0 + x4 = -20x2 + 20x2 + x4
x4 = -20x2 + 20x2 + x4

Combine like terms: -20x2 + 20x2 = 0
x4 = 0 + x4
x4 = x4

Add '-1x4' to each side of the equation.
x4 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
0 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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