X^6+15x^5+78x^4+155x^3+78x^2+15x+1=0

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Solution for X^6+15x^5+78x^4+155x^3+78x^2+15x+1=0 equation: 


Simplifying
X6 + 15x5 + 78x4 + 155x3 + 78x2 + 15x + 1 = 0

Reorder the terms:
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0

Solving
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0

Solving for variable 'X'.

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

Add '-1' to each side of the equation.
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + -1 + 15x5 = 0 + -1

Reorder the terms:
1 + -1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0 + -1
X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0 + -1

Combine like terms: 0 + -1 = -1
X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = -1

Add '-15x' to each side of the equation.
X6 + 15x + 78x2 + 155x3 + 78x4 + -15x + 15x5 = -1 + -15x

Reorder the terms:
X6 + 15x + -15x + 78x2 + 155x3 + 78x4 + 15x5 = -1 + -15x

Combine like terms: 15x + -15x = 0
X6 + 0 + 78x2 + 155x3 + 78x4 + 15x5 = -1 + -15x
X6 + 78x2 + 155x3 + 78x4 + 15x5 = -1 + -15x

Add '-78x2' to each side of the equation.
X6 + 78x2 + 155x3 + 78x4 + -78x2 + 15x5 = -1 + -15x + -78x2

Reorder the terms:
X6 + 78x2 + -78x2 + 155x3 + 78x4 + 15x5 = -1 + -15x + -78x2

Combine like terms: 78x2 + -78x2 = 0
X6 + 0 + 155x3 + 78x4 + 15x5 = -1 + -15x + -78x2
X6 + 155x3 + 78x4 + 15x5 = -1 + -15x + -78x2

Add '-155x3' to each side of the equation.
X6 + 155x3 + 78x4 + -155x3 + 15x5 = -1 + -15x + -78x2 + -155x3

Reorder the terms:
X6 + 155x3 + -155x3 + 78x4 + 15x5 = -1 + -15x + -78x2 + -155x3

Combine like terms: 155x3 + -155x3 = 0
X6 + 0 + 78x4 + 15x5 = -1 + -15x + -78x2 + -155x3
X6 + 78x4 + 15x5 = -1 + -15x + -78x2 + -155x3

Add '-78x4' to each side of the equation.
X6 + 78x4 + -78x4 + 15x5 = -1 + -15x + -78x2 + -155x3 + -78x4

Combine like terms: 78x4 + -78x4 = 0
X6 + 0 + 15x5 = -1 + -15x + -78x2 + -155x3 + -78x4
X6 + 15x5 = -1 + -15x + -78x2 + -155x3 + -78x4

Add '-15x5' to each side of the equation.
X6 + 15x5 + -15x5 = -1 + -15x + -78x2 + -155x3 + -78x4 + -15x5

Combine like terms: 15x5 + -15x5 = 0
X6 + 0 = -1 + -15x + -78x2 + -155x3 + -78x4 + -15x5
X6 = -1 + -15x + -78x2 + -155x3 + -78x4 + -15x5

Simplifying
X6 = -1 + -15x + -78x2 + -155x3 + -78x4 + -15x5

Reorder the terms:
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = -1 + -15x + -78x2 + -155x3 + -78x4 + -15x5 + 1 + 15x + 78x2 + 155x3 + 78x4 + 15x5

Reorder the terms:
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = -1 + 1 + -15x + 15x + -78x2 + 78x2 + -155x3 + 155x3 + -78x4 + 78x4 + -15x5 + 15x5

Combine like terms: -1 + 1 = 0
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0 + -15x + 15x + -78x2 + 78x2 + -155x3 + 155x3 + -78x4 + 78x4 + -15x5 + 15x5
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = -15x + 15x + -78x2 + 78x2 + -155x3 + 155x3 + -78x4 + 78x4 + -15x5 + 15x5

Combine like terms: -15x + 15x = 0
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0 + -78x2 + 78x2 + -155x3 + 155x3 + -78x4 + 78x4 + -15x5 + 15x5
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = -78x2 + 78x2 + -155x3 + 155x3 + -78x4 + 78x4 + -15x5 + 15x5

Combine like terms: -78x2 + 78x2 = 0
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0 + -155x3 + 155x3 + -78x4 + 78x4 + -15x5 + 15x5
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = -155x3 + 155x3 + -78x4 + 78x4 + -15x5 + 15x5

Combine like terms: -155x3 + 155x3 = 0
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0 + -78x4 + 78x4 + -15x5 + 15x5
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = -78x4 + 78x4 + -15x5 + 15x5

Combine like terms: -78x4 + 78x4 = 0
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0 + -15x5 + 15x5
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = -15x5 + 15x5

Combine like terms: -15x5 + 15x5 = 0
1 + X6 + 15x + 78x2 + 155x3 + 78x4 + 15x5 = 0

The solution to this equation could not be determined.

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