(x+2)(x+2)(x+6)(x+6)(x+6)+(x+2)(x+6)(x+6)(x+6)(x+6)=0

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Solution for (x+2)(x+2)(x+6)(x+6)(x+6)+(x+2)(x+6)(x+6)(x+6)(x+6)=0 equation: 


Simplifying
(x + 2)(x + 2)(x + 6)(x + 6)(x + 6) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Reorder the terms:
(2 + x)(x + 2)(x + 6)(x + 6)(x + 6) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Reorder the terms:
(2 + x)(2 + x)(x + 6)(x + 6)(x + 6) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Reorder the terms:
(2 + x)(2 + x)(6 + x)(x + 6)(x + 6) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Reorder the terms:
(2 + x)(2 + x)(6 + x)(6 + x)(x + 6) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Reorder the terms:
(2 + x)(2 + x)(6 + x)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x))(6 + x)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
((2 * 2 + x * 2) + x(2 + x))(6 + x)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
((4 + 2x) + x(2 + x))(6 + x)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(4 + 2x + (2 * x + x * x))(6 + x)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(4 + 2x + (2x + x2))(6 + x)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2)(6 + x)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Multiply (4 + 4x + x2) * (6 + x)
(4(6 + x) + 4x * (6 + x) + x2(6 + x))(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
((6 * 4 + x * 4) + 4x * (6 + x) + x2(6 + x))(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
((24 + 4x) + 4x * (6 + x) + x2(6 + x))(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(24 + 4x + (6 * 4x + x * 4x) + x2(6 + x))(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(24 + 4x + (24x + 4x2) + x2(6 + x))(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(24 + 4x + 24x + 4x2 + (6 * x2 + x * x2))(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(24 + 4x + 24x + 4x2 + (6x2 + x3))(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 4x + 24x = 28x
(24 + 28x + 4x2 + 6x2 + x3)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 4x2 + 6x2 = 10x2
(24 + 28x + 10x2 + x3)(6 + x)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Multiply (24 + 28x + 10x2 + x3) * (6 + x)
(24(6 + x) + 28x * (6 + x) + 10x2 * (6 + x) + x3(6 + x))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
((6 * 24 + x * 24) + 28x * (6 + x) + 10x2 * (6 + x) + x3(6 + x))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
((144 + 24x) + 28x * (6 + x) + 10x2 * (6 + x) + x3(6 + x))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(144 + 24x + (6 * 28x + x * 28x) + 10x2 * (6 + x) + x3(6 + x))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(144 + 24x + (168x + 28x2) + 10x2 * (6 + x) + x3(6 + x))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(144 + 24x + 168x + 28x2 + (6 * 10x2 + x * 10x2) + x3(6 + x))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(144 + 24x + 168x + 28x2 + (60x2 + 10x3) + x3(6 + x))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(144 + 24x + 168x + 28x2 + 60x2 + 10x3 + (6 * x3 + x * x3))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(144 + 24x + 168x + 28x2 + 60x2 + 10x3 + (6x3 + x4))(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 24x + 168x = 192x
(144 + 192x + 28x2 + 60x2 + 10x3 + 6x3 + x4)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 28x2 + 60x2 = 88x2
(144 + 192x + 88x2 + 10x3 + 6x3 + x4)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 10x3 + 6x3 = 16x3
(144 + 192x + 88x2 + 16x3 + x4)(6 + x) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Multiply (144 + 192x + 88x2 + 16x3 + x4) * (6 + x)
(144(6 + x) + 192x * (6 + x) + 88x2 * (6 + x) + 16x3 * (6 + x) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
((6 * 144 + x * 144) + 192x * (6 + x) + 88x2 * (6 + x) + 16x3 * (6 + x) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
((864 + 144x) + 192x * (6 + x) + 88x2 * (6 + x) + 16x3 * (6 + x) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(864 + 144x + (6 * 192x + x * 192x) + 88x2 * (6 + x) + 16x3 * (6 + x) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(864 + 144x + (1152x + 192x2) + 88x2 * (6 + x) + 16x3 * (6 + x) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(864 + 144x + 1152x + 192x2 + (6 * 88x2 + x * 88x2) + 16x3 * (6 + x) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(864 + 144x + 1152x + 192x2 + (528x2 + 88x3) + 16x3 * (6 + x) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(864 + 144x + 1152x + 192x2 + 528x2 + 88x3 + (6 * 16x3 + x * 16x3) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(864 + 144x + 1152x + 192x2 + 528x2 + 88x3 + (96x3 + 16x4) + x4(6 + x)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(864 + 144x + 1152x + 192x2 + 528x2 + 88x3 + 96x3 + 16x4 + (6 * x4 + x * x4)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0
(864 + 144x + 1152x + 192x2 + 528x2 + 88x3 + 96x3 + 16x4 + (6x4 + x5)) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 144x + 1152x = 1296x
(864 + 1296x + 192x2 + 528x2 + 88x3 + 96x3 + 16x4 + 6x4 + x5) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 192x2 + 528x2 = 720x2
(864 + 1296x + 720x2 + 88x3 + 96x3 + 16x4 + 6x4 + x5) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 88x3 + 96x3 = 184x3
(864 + 1296x + 720x2 + 184x3 + 16x4 + 6x4 + x5) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Combine like terms: 16x4 + 6x4 = 22x4
(864 + 1296x + 720x2 + 184x3 + 22x4 + x5) + (x + 2)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Reorder the terms:
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2 + x)(x + 6)(x + 6)(x + 6)(x + 6) = 0

Reorder the terms:
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2 + x)(6 + x)(x + 6)(x + 6)(x + 6) = 0

Reorder the terms:
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2 + x)(6 + x)(6 + x)(x + 6)(x + 6) = 0

Reorder the terms:
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2 + x)(6 + x)(6 + x)(6 + x)(x + 6) = 0

Reorder the terms:
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2 + x)(6 + x)(6 + x)(6 + x)(6 + x) = 0

Multiply (2 + x) * (6 + x)
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2(6 + x) + x(6 + x))(6 + x)(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + ((6 * 2 + x * 2) + x(6 + x))(6 + x)(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + ((12 + 2x) + x(6 + x))(6 + x)(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (12 + 2x + (6 * x + x * x))(6 + x)(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (12 + 2x + (6x + x2))(6 + x)(6 + x)(6 + x) = 0

Combine like terms: 2x + 6x = 8x
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (12 + 8x + x2)(6 + x)(6 + x)(6 + x) = 0

Multiply (12 + 8x + x2) * (6 + x)
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (12(6 + x) + 8x * (6 + x) + x2(6 + x))(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + ((6 * 12 + x * 12) + 8x * (6 + x) + x2(6 + x))(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + ((72 + 12x) + 8x * (6 + x) + x2(6 + x))(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (72 + 12x + (6 * 8x + x * 8x) + x2(6 + x))(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (72 + 12x + (48x + 8x2) + x2(6 + x))(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (72 + 12x + 48x + 8x2 + (6 * x2 + x * x2))(6 + x)(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (72 + 12x + 48x + 8x2 + (6x2 + x3))(6 + x)(6 + x) = 0

Combine like terms: 12x + 48x = 60x
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (72 + 60x + 8x2 + 6x2 + x3)(6 + x)(6 + x) = 0

Combine like terms: 8x2 + 6x2 = 14x2
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (72 + 60x + 14x2 + x3)(6 + x)(6 + x) = 0

Multiply (72 + 60x + 14x2 + x3) * (6 + x)
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (72(6 + x) + 60x * (6 + x) + 14x2 * (6 + x) + x3(6 + x))(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + ((6 * 72 + x * 72) + 60x * (6 + x) + 14x2 * (6 + x) + x3(6 + x))(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + ((432 + 72x) + 60x * (6 + x) + 14x2 * (6 + x) + x3(6 + x))(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 72x + (6 * 60x + x * 60x) + 14x2 * (6 + x) + x3(6 + x))(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 72x + (360x + 60x2) + 14x2 * (6 + x) + x3(6 + x))(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 72x + 360x + 60x2 + (6 * 14x2 + x * 14x2) + x3(6 + x))(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 72x + 360x + 60x2 + (84x2 + 14x3) + x3(6 + x))(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 72x + 360x + 60x2 + 84x2 + 14x3 + (6 * x3 + x * x3))(6 + x) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 72x + 360x + 60x2 + 84x2 + 14x3 + (6x3 + x4))(6 + x) = 0

Combine like terms: 72x + 360x = 432x
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 432x + 60x2 + 84x2 + 14x3 + 6x3 + x4)(6 + x) = 0

Combine like terms: 60x2 + 84x2 = 144x2
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 432x + 144x2 + 14x3 + 6x3 + x4)(6 + x) = 0

Combine like terms: 14x3 + 6x3 = 20x3
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432 + 432x + 144x2 + 20x3 + x4)(6 + x) = 0

Multiply (432 + 432x + 144x2 + 20x3 + x4) * (6 + x)
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (432(6 + x) + 432x * (6 + x) + 144x2 * (6 + x) + 20x3 * (6 + x) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + ((6 * 432 + x * 432) + 432x * (6 + x) + 144x2 * (6 + x) + 20x3 * (6 + x) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + ((2592 + 432x) + 432x * (6 + x) + 144x2 * (6 + x) + 20x3 * (6 + x) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 432x + (6 * 432x + x * 432x) + 144x2 * (6 + x) + 20x3 * (6 + x) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 432x + (2592x + 432x2) + 144x2 * (6 + x) + 20x3 * (6 + x) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 432x + 2592x + 432x2 + (6 * 144x2 + x * 144x2) + 20x3 * (6 + x) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 432x + 2592x + 432x2 + (864x2 + 144x3) + 20x3 * (6 + x) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 432x + 2592x + 432x2 + 864x2 + 144x3 + (6 * 20x3 + x * 20x3) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 432x + 2592x + 432x2 + 864x2 + 144x3 + (120x3 + 20x4) + x4(6 + x)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 432x + 2592x + 432x2 + 864x2 + 144x3 + 120x3 + 20x4 + (6 * x4 + x * x4)) = 0
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 432x + 2592x + 432x2 + 864x2 + 144x3 + 120x3 + 20x4 + (6x4 + x5)) = 0

Combine like terms: 432x + 2592x = 3024x
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 3024x + 432x2 + 864x2 + 144x3 + 120x3 + 20x4 + 6x4 + x5) = 0

Combine like terms: 432x2 + 864x2 = 1296x2
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 3024x + 1296x2 + 144x3 + 120x3 + 20x4 + 6x4 + x5) = 0

Combine like terms: 144x3 + 120x3 = 264x3
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 3024x + 1296x2 + 264x3 + 20x4 + 6x4 + x5) = 0

Combine like terms: 20x4 + 6x4 = 26x4
864 + 1296x + 720x2 + 184x3 + 22x4 + x5 + (2592 + 3024x + 1296x2 + 264x3 + 26x4 + x5) = 0

Reorder the terms:
864 + 2592 + 1296x + 3024x + 720x2 + 1296x2 + 184x3 + 264x3 + 22x4 + 26x4 + x5 + x5 = 0

Combine like terms: 864 + 2592 = 3456
3456 + 1296x + 3024x + 720x2 + 1296x2 + 184x3 + 264x3 + 22x4 + 26x4 + x5 + x5 = 0

Combine like terms: 1296x + 3024x = 4320x
3456 + 4320x + 720x2 + 1296x2 + 184x3 + 264x3 + 22x4 + 26x4 + x5 + x5 = 0

Combine like terms: 720x2 + 1296x2 = 2016x2
3456 + 4320x + 2016x2 + 184x3 + 264x3 + 22x4 + 26x4 + x5 + x5 = 0

Combine like terms: 184x3 + 264x3 = 448x3
3456 + 4320x + 2016x2 + 448x3 + 22x4 + 26x4 + x5 + x5 = 0

Combine like terms: 22x4 + 26x4 = 48x4
3456 + 4320x + 2016x2 + 448x3 + 48x4 + x5 + x5 = 0

Combine like terms: x5 + x5 = 2x5
3456 + 4320x + 2016x2 + 448x3 + 48x4 + 2x5 = 0

Solving
3456 + 4320x + 2016x2 + 448x3 + 48x4 + 2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1728 + 2160x + 1008x2 + 224x3 + 24x4 + x5) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1728 + 2160x + 1008x2 + 224x3 + 24x4 + x5)' equal to zero and attempt to solve:

Simplifying
1728 + 2160x + 1008x2 + 224x3 + 24x4 + x5 = 0

Solving
1728 + 2160x + 1008x2 + 224x3 + 24x4 + x5 = 0

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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