z^4=5(z-1)(z^2-z+1)

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Solution for z^4=5(z-1)(z^2-z+1) equation: 


Simplifying
z4 = 5(z + -1)(z2 + -1z + 1)

Reorder the terms:
z4 = 5(-1 + z)(z2 + -1z + 1)

Reorder the terms:
z4 = 5(-1 + z)(1 + -1z + z2)

Multiply (-1 + z) * (1 + -1z + z2)
z4 = 5(-1(1 + -1z + z2) + z(1 + -1z + z2))
z4 = 5((1 * -1 + -1z * -1 + z2 * -1) + z(1 + -1z + z2))
z4 = 5((-1 + 1z + -1z2) + z(1 + -1z + z2))
z4 = 5(-1 + 1z + -1z2 + (1 * z + -1z * z + z2 * z))
z4 = 5(-1 + 1z + -1z2 + (1z + -1z2 + z3))

Reorder the terms:
z4 = 5(-1 + 1z + 1z + -1z2 + -1z2 + z3)

Combine like terms: 1z + 1z = 2z
z4 = 5(-1 + 2z + -1z2 + -1z2 + z3)

Combine like terms: -1z2 + -1z2 = -2z2
z4 = 5(-1 + 2z + -2z2 + z3)
z4 = (-1 * 5 + 2z * 5 + -2z2 * 5 + z3 * 5)
z4 = (-5 + 10z + -10z2 + 5z3)

Solving
z4 = -5 + 10z + -10z2 + 5z3

Solving for variable 'z'.

Reorder the terms:
5 + -10z + 10z2 + -5z3 + z4 = -5 + 10z + -10z2 + 5z3 + 5 + -10z + 10z2 + -5z3

Reorder the terms:
5 + -10z + 10z2 + -5z3 + z4 = -5 + 5 + 10z + -10z + -10z2 + 10z2 + 5z3 + -5z3

Combine like terms: -5 + 5 = 0
5 + -10z + 10z2 + -5z3 + z4 = 0 + 10z + -10z + -10z2 + 10z2 + 5z3 + -5z3
5 + -10z + 10z2 + -5z3 + z4 = 10z + -10z + -10z2 + 10z2 + 5z3 + -5z3

Combine like terms: 10z + -10z = 0
5 + -10z + 10z2 + -5z3 + z4 = 0 + -10z2 + 10z2 + 5z3 + -5z3
5 + -10z + 10z2 + -5z3 + z4 = -10z2 + 10z2 + 5z3 + -5z3

Combine like terms: -10z2 + 10z2 = 0
5 + -10z + 10z2 + -5z3 + z4 = 0 + 5z3 + -5z3
5 + -10z + 10z2 + -5z3 + z4 = 5z3 + -5z3

Combine like terms: 5z3 + -5z3 = 0
5 + -10z + 10z2 + -5z3 + z4 = 0

The solution to this equation could not be determined.

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