=(a+b+c)(a+b+c)(a+b+c)

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Solution for =(a+b+c)(a+b+c)(a+b+c) equation: 


Simplifying
0 = (a + b + c)(a + b + c)(a + b + c)

Multiply (a + b + c) * (a + b + c)
0 = (a(a + b + c) + b(a + b + c) + c(a + b + c))(a + b + c)
0 = ((a * a + b * a + c * a) + b(a + b + c) + c(a + b + c))(a + b + c)

Reorder the terms:
0 = ((ab + ac + a2) + b(a + b + c) + c(a + b + c))(a + b + c)
0 = ((ab + ac + a2) + b(a + b + c) + c(a + b + c))(a + b + c)
0 = (ab + ac + a2 + (a * b + b * b + c * b) + c(a + b + c))(a + b + c)

Reorder the terms:
0 = (ab + ac + a2 + (ab + bc + b2) + c(a + b + c))(a + b + c)
0 = (ab + ac + a2 + (ab + bc + b2) + c(a + b + c))(a + b + c)
0 = (ab + ac + a2 + ab + bc + b2 + (a * c + b * c + c * c))(a + b + c)
0 = (ab + ac + a2 + ab + bc + b2 + (ac + bc + c2))(a + b + c)

Reorder the terms:
0 = (ab + ab + ac + ac + a2 + bc + bc + b2 + c2)(a + b + c)

Combine like terms: ab + ab = 2ab
0 = (2ab + ac + ac + a2 + bc + bc + b2 + c2)(a + b + c)

Combine like terms: ac + ac = 2ac
0 = (2ab + 2ac + a2 + bc + bc + b2 + c2)(a + b + c)

Combine like terms: bc + bc = 2bc
0 = (2ab + 2ac + a2 + 2bc + b2 + c2)(a + b + c)

Multiply (2ab + 2ac + a2 + 2bc + b2 + c2) * (a + b + c)
0 = (2ab * (a + b + c) + 2ac * (a + b + c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))
0 = ((a * 2ab + b * 2ab + c * 2ab) + 2ac * (a + b + c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))

Reorder the terms:
0 = ((2abc + 2ab2 + 2a2b) + 2ac * (a + b + c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))
0 = ((2abc + 2ab2 + 2a2b) + 2ac * (a + b + c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + (a * 2ac + b * 2ac + c * 2ac) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))

Reorder the terms:
0 = (2abc + 2ab2 + 2a2b + (2abc + 2ac2 + 2a2c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + (2abc + 2ac2 + 2a2c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + (a * a2 + b * a2 + c * a2) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))

Reorder the terms:
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + (a2b + a2c + a3) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + (a2b + a2c + a3) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + (a * 2bc + b * 2bc + c * 2bc) + b2(a + b + c) + c2(a + b + c))

Reorder the terms:
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + (2abc + 2bc2 + 2b2c) + b2(a + b + c) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + (2abc + 2bc2 + 2b2c) + b2(a + b + c) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + (a * b2 + b * b2 + c * b2) + c2(a + b + c))

Reorder the terms:
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + (ab2 + b2c + b3) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + (ab2 + b2c + b3) + c2(a + b + c))
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + ab2 + b2c + b3 + (a * c2 + b * c2 + c * c2))
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + ab2 + b2c + b3 + (ac2 + bc2 + c3))

Reorder the terms:
0 = (2abc + 2abc + 2abc + 2ab2 + ab2 + 2ac2 + ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)

Combine like terms: 2abc + 2abc = 4abc
0 = (4abc + 2abc + 2ab2 + ab2 + 2ac2 + ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)

Combine like terms: 4abc + 2abc = 6abc
0 = (6abc + 2ab2 + ab2 + 2ac2 + ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)

Combine like terms: 2ab2 + ab2 = 3ab2
0 = (6abc + 3ab2 + 2ac2 + ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)

Combine like terms: 2ac2 + ac2 = 3ac2
0 = (6abc + 3ab2 + 3ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)

Combine like terms: 2a2b + a2b = 3a2b
0 = (6abc + 3ab2 + 3ac2 + 3a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)

Combine like terms: 2a2c + a2c = 3a2c
0 = (6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)

Combine like terms: 2bc2 + bc2 = 3bc2
0 = (6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 2b2c + b2c + b3 + c3)

Combine like terms: 2b2c + b2c = 3b2c
0 = (6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3)

Solving
0 = 6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3

Solving for variable 'a'.
Remove the zero:
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3 + -6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3

Reorder the terms:
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 6abc + -6abc + 3ab2 + -3ab2 + 3ac2 + -3ac2 + 3a2b + -3a2b + 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3

Combine like terms: 6abc + -6abc = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + 3ab2 + -3ab2 + 3ac2 + -3ac2 + 3a2b + -3a2b + 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 3ab2 + -3ab2 + 3ac2 + -3ac2 + 3a2b + -3a2b + 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3

Combine like terms: 3ab2 + -3ab2 = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + 3ac2 + -3ac2 + 3a2b + -3a2b + 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 3ac2 + -3ac2 + 3a2b + -3a2b + 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3

Combine like terms: 3ac2 + -3ac2 = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + 3a2b + -3a2b + 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 3a2b + -3a2b + 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3

Combine like terms: 3a2b + -3a2b = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 3a2c + -3a2c + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3

Combine like terms: 3a2c + -3a2c = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = a3 + -1a3 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3

Combine like terms: a3 + -1a3 = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 3bc2 + -3bc2 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3

Combine like terms: 3bc2 + -3bc2 = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 3b2c + -3b2c + b3 + -1b3 + c3 + -1c3

Combine like terms: 3b2c + -3b2c = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + b3 + -1b3 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = b3 + -1b3 + c3 + -1c3

Combine like terms: b3 + -1b3 = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0 + c3 + -1c3
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = c3 + -1c3

Combine like terms: c3 + -1c3 = 0
-6abc + -3ab2 + -3ac2 + -3a2b + -3a2c + -1a3 + -3bc2 + -3b2c + -1b3 + -1c3 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3)' equal to zero and attempt to solve:

Simplifying
6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3 = 0

Solving
6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3 = 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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