(a+b+c)(a^2+b^2+c^2)=9abc

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Solution for (a+b+c)(a^2+b^2+c^2)=9abc equation: 


Simplifying
(a + b + c)(a2 + b2 + c2) = 9abc

Multiply (a + b + c) * (a2 + b2 + c2)
(a(a2 + b2 + c2) + b(a2 + b2 + c2) + c(a2 + b2 + c2)) = 9abc
((a2 * a + b2 * a + c2 * a) + b(a2 + b2 + c2) + c(a2 + b2 + c2)) = 9abc

Reorder the terms:
((ab2 + ac2 + a3) + b(a2 + b2 + c2) + c(a2 + b2 + c2)) = 9abc
((ab2 + ac2 + a3) + b(a2 + b2 + c2) + c(a2 + b2 + c2)) = 9abc
(ab2 + ac2 + a3 + (a2 * b + b2 * b + c2 * b) + c(a2 + b2 + c2)) = 9abc

Reorder the terms:
(ab2 + ac2 + a3 + (a2b + bc2 + b3) + c(a2 + b2 + c2)) = 9abc
(ab2 + ac2 + a3 + (a2b + bc2 + b3) + c(a2 + b2 + c2)) = 9abc
(ab2 + ac2 + a3 + a2b + bc2 + b3 + (a2 * c + b2 * c + c2 * c)) = 9abc
(ab2 + ac2 + a3 + a2b + bc2 + b3 + (a2c + b2c + c3)) = 9abc

Reorder the terms:
(ab2 + ac2 + a2b + a2c + a3 + bc2 + b2c + b3 + c3) = 9abc
(ab2 + ac2 + a2b + a2c + a3 + bc2 + b2c + b3 + c3) = 9abc

Solving
ab2 + ac2 + a2b + a2c + a3 + bc2 + b2c + b3 + c3 = 9abc

Solving for variable 'a'.

Reorder the terms:
-9abc + ab2 + ac2 + a2b + a2c + a3 + bc2 + b2c + b3 + c3 = 9abc + -9abc

Combine like terms: 9abc + -9abc = 0
-9abc + ab2 + ac2 + a2b + a2c + a3 + bc2 + b2c + b3 + c3 = 0

The solution to this equation could not be determined.

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