a^6+b^6+c^6=2(a^5+b^5+c^5)+abc(a^3+b^3+c^3)

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Solution for a^6+b^6+c^6=2(a^5+b^5+c^5)+abc(a^3+b^3+c^3) equation: 


Simplifying
a6 + b6 + c6 = 2(a5 + b5 + c5) + abc(a3 + b3 + c3)
a6 + b6 + c6 = (a5 * 2 + b5 * 2 + c5 * 2) + abc(a3 + b3 + c3)
a6 + b6 + c6 = (2a5 + 2b5 + 2c5) + abc(a3 + b3 + c3)
a6 + b6 + c6 = 2a5 + 2b5 + 2c5 + (a3 * abc + b3 * abc + c3 * abc)

Reorder the terms:
a6 + b6 + c6 = 2a5 + 2b5 + 2c5 + (abc4 + ab4c + a4bc)
a6 + b6 + c6 = 2a5 + 2b5 + 2c5 + (abc4 + ab4c + a4bc)

Reorder the terms:
a6 + b6 + c6 = abc4 + ab4c + a4bc + 2a5 + 2b5 + 2c5

Solving
a6 + b6 + c6 = abc4 + ab4c + a4bc + 2a5 + 2b5 + 2c5

Solving for variable 'a'.

Reorder the terms:
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = abc4 + ab4c + a4bc + 2a5 + 2b5 + 2c5 + -1abc4 + -1ab4c + -1a4bc + -2a5 + -2b5 + -2c5

Reorder the terms:
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = abc4 + -1abc4 + ab4c + -1ab4c + a4bc + -1a4bc + 2a5 + -2a5 + 2b5 + -2b5 + 2c5 + -2c5

Combine like terms: abc4 + -1abc4 = 0
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 0 + ab4c + -1ab4c + a4bc + -1a4bc + 2a5 + -2a5 + 2b5 + -2b5 + 2c5 + -2c5
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = ab4c + -1ab4c + a4bc + -1a4bc + 2a5 + -2a5 + 2b5 + -2b5 + 2c5 + -2c5

Combine like terms: ab4c + -1ab4c = 0
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 0 + a4bc + -1a4bc + 2a5 + -2a5 + 2b5 + -2b5 + 2c5 + -2c5
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = a4bc + -1a4bc + 2a5 + -2a5 + 2b5 + -2b5 + 2c5 + -2c5

Combine like terms: a4bc + -1a4bc = 0
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 0 + 2a5 + -2a5 + 2b5 + -2b5 + 2c5 + -2c5
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 2a5 + -2a5 + 2b5 + -2b5 + 2c5 + -2c5

Combine like terms: 2a5 + -2a5 = 0
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 0 + 2b5 + -2b5 + 2c5 + -2c5
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 2b5 + -2b5 + 2c5 + -2c5

Combine like terms: 2b5 + -2b5 = 0
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 0 + 2c5 + -2c5
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 2c5 + -2c5

Combine like terms: 2c5 + -2c5 = 0
-1abc4 + -1ab4c + -1a4bc + -2a5 + a6 + -2b5 + b6 + -2c5 + c6 = 0

The solution to this equation could not be determined.

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