Tk=(2k-1)(2k-1)(2k-1)

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Solution for Tk=(2k-1)(2k-1)(2k-1) equation: 


Simplifying
Tk = (2k + -1)(2k + -1)(2k + -1)

Reorder the terms:
kT = (-1 + 2k)(2k + -1)(2k + -1)

Reorder the terms:
kT = (-1 + 2k)(-1 + 2k)(2k + -1)

Reorder the terms:
kT = (-1 + 2k)(-1 + 2k)(-1 + 2k)

Multiply (-1 + 2k) * (-1 + 2k)
kT = (-1(-1 + 2k) + 2k * (-1 + 2k))(-1 + 2k)
kT = ((-1 * -1 + 2k * -1) + 2k * (-1 + 2k))(-1 + 2k)
kT = ((1 + -2k) + 2k * (-1 + 2k))(-1 + 2k)
kT = (1 + -2k + (-1 * 2k + 2k * 2k))(-1 + 2k)
kT = (1 + -2k + (-2k + 4k2))(-1 + 2k)

Combine like terms: -2k + -2k = -4k
kT = (1 + -4k + 4k2)(-1 + 2k)

Multiply (1 + -4k + 4k2) * (-1 + 2k)
kT = (1(-1 + 2k) + -4k * (-1 + 2k) + 4k2 * (-1 + 2k))
kT = ((-1 * 1 + 2k * 1) + -4k * (-1 + 2k) + 4k2 * (-1 + 2k))
kT = ((-1 + 2k) + -4k * (-1 + 2k) + 4k2 * (-1 + 2k))
kT = (-1 + 2k + (-1 * -4k + 2k * -4k) + 4k2 * (-1 + 2k))
kT = (-1 + 2k + (4k + -8k2) + 4k2 * (-1 + 2k))
kT = (-1 + 2k + 4k + -8k2 + (-1 * 4k2 + 2k * 4k2))
kT = (-1 + 2k + 4k + -8k2 + (-4k2 + 8k3))

Combine like terms: 2k + 4k = 6k
kT = (-1 + 6k + -8k2 + -4k2 + 8k3)

Combine like terms: -8k2 + -4k2 = -12k2
kT = (-1 + 6k + -12k2 + 8k3)

Solving
kT = -1 + 6k + -12k2 + 8k3

Solving for variable 'k'.

Reorder the terms:
1 + -6k + kT + 12k2 + -8k3 = -1 + 6k + -12k2 + 8k3 + 1 + -6k + 12k2 + -8k3

Reorder the terms:
1 + -6k + kT + 12k2 + -8k3 = -1 + 1 + 6k + -6k + -12k2 + 12k2 + 8k3 + -8k3

Combine like terms: -1 + 1 = 0
1 + -6k + kT + 12k2 + -8k3 = 0 + 6k + -6k + -12k2 + 12k2 + 8k3 + -8k3
1 + -6k + kT + 12k2 + -8k3 = 6k + -6k + -12k2 + 12k2 + 8k3 + -8k3

Combine like terms: 6k + -6k = 0
1 + -6k + kT + 12k2 + -8k3 = 0 + -12k2 + 12k2 + 8k3 + -8k3
1 + -6k + kT + 12k2 + -8k3 = -12k2 + 12k2 + 8k3 + -8k3

Combine like terms: -12k2 + 12k2 = 0
1 + -6k + kT + 12k2 + -8k3 = 0 + 8k3 + -8k3
1 + -6k + kT + 12k2 + -8k3 = 8k3 + -8k3

Combine like terms: 8k3 + -8k3 = 0
1 + -6k + kT + 12k2 + -8k3 = 0

The solution to this equation could not be determined.

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