(x^2+2k+1)*(2x^2+4k+1)=2k^4-k^2+2k^3+1

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Solution for (x^2+2k+1)*(2x^2+4k+1)=2k^4-k^2+2k^3+1 equation: 


Simplifying
(x2 + 2k + 1)(2x2 + 4k + 1) = 2k4 + -1k2 + 2k3 + 1

Reorder the terms:
(1 + 2k + x2)(2x2 + 4k + 1) = 2k4 + -1k2 + 2k3 + 1

Reorder the terms:
(1 + 2k + x2)(1 + 4k + 2x2) = 2k4 + -1k2 + 2k3 + 1

Multiply (1 + 2k + x2) * (1 + 4k + 2x2)
(1(1 + 4k + 2x2) + 2k * (1 + 4k + 2x2) + x2(1 + 4k + 2x2)) = 2k4 + -1k2 + 2k3 + 1
((1 * 1 + 4k * 1 + 2x2 * 1) + 2k * (1 + 4k + 2x2) + x2(1 + 4k + 2x2)) = 2k4 + -1k2 + 2k3 + 1
((1 + 4k + 2x2) + 2k * (1 + 4k + 2x2) + x2(1 + 4k + 2x2)) = 2k4 + -1k2 + 2k3 + 1
(1 + 4k + 2x2 + (1 * 2k + 4k * 2k + 2x2 * 2k) + x2(1 + 4k + 2x2)) = 2k4 + -1k2 + 2k3 + 1

Reorder the terms:
(1 + 4k + 2x2 + (2k + 4kx2 + 8k2) + x2(1 + 4k + 2x2)) = 2k4 + -1k2 + 2k3 + 1
(1 + 4k + 2x2 + (2k + 4kx2 + 8k2) + x2(1 + 4k + 2x2)) = 2k4 + -1k2 + 2k3 + 1
(1 + 4k + 2x2 + 2k + 4kx2 + 8k2 + (1 * x2 + 4k * x2 + 2x2 * x2)) = 2k4 + -1k2 + 2k3 + 1

Reorder the terms:
(1 + 4k + 2x2 + 2k + 4kx2 + 8k2 + (4kx2 + 1x2 + 2x4)) = 2k4 + -1k2 + 2k3 + 1
(1 + 4k + 2x2 + 2k + 4kx2 + 8k2 + (4kx2 + 1x2 + 2x4)) = 2k4 + -1k2 + 2k3 + 1

Reorder the terms:
(1 + 4k + 2k + 4kx2 + 4kx2 + 8k2 + 2x2 + 1x2 + 2x4) = 2k4 + -1k2 + 2k3 + 1

Combine like terms: 4k + 2k = 6k
(1 + 6k + 4kx2 + 4kx2 + 8k2 + 2x2 + 1x2 + 2x4) = 2k4 + -1k2 + 2k3 + 1

Combine like terms: 4kx2 + 4kx2 = 8kx2
(1 + 6k + 8kx2 + 8k2 + 2x2 + 1x2 + 2x4) = 2k4 + -1k2 + 2k3 + 1

Combine like terms: 2x2 + 1x2 = 3x2
(1 + 6k + 8kx2 + 8k2 + 3x2 + 2x4) = 2k4 + -1k2 + 2k3 + 1

Reorder the terms:
1 + 6k + 8kx2 + 8k2 + 3x2 + 2x4 = 1 + -1k2 + 2k3 + 2k4

Add '-1' to each side of the equation.
1 + 6k + 8kx2 + 8k2 + 3x2 + -1 + 2x4 = 1 + -1k2 + 2k3 + -1 + 2k4

Reorder the terms:
1 + -1 + 6k + 8kx2 + 8k2 + 3x2 + 2x4 = 1 + -1k2 + 2k3 + -1 + 2k4

Combine like terms: 1 + -1 = 0
0 + 6k + 8kx2 + 8k2 + 3x2 + 2x4 = 1 + -1k2 + 2k3 + -1 + 2k4
6k + 8kx2 + 8k2 + 3x2 + 2x4 = 1 + -1k2 + 2k3 + -1 + 2k4

Reorder the terms:
6k + 8kx2 + 8k2 + 3x2 + 2x4 = 1 + -1 + -1k2 + 2k3 + 2k4

Combine like terms: 1 + -1 = 0
6k + 8kx2 + 8k2 + 3x2 + 2x4 = 0 + -1k2 + 2k3 + 2k4
6k + 8kx2 + 8k2 + 3x2 + 2x4 = -1k2 + 2k3 + 2k4

Solving
6k + 8kx2 + 8k2 + 3x2 + 2x4 = -1k2 + 2k3 + 2k4

Solving for variable 'k'.

Reorder the terms:
6k + 8kx2 + 8k2 + k2 + -2k3 + -2k4 + 3x2 + 2x4 = -1k2 + 2k3 + 2k4 + k2 + -2k3 + -2k4

Combine like terms: 8k2 + k2 = 9k2
6k + 8kx2 + 9k2 + -2k3 + -2k4 + 3x2 + 2x4 = -1k2 + 2k3 + 2k4 + k2 + -2k3 + -2k4

Reorder the terms:
6k + 8kx2 + 9k2 + -2k3 + -2k4 + 3x2 + 2x4 = -1k2 + k2 + 2k3 + -2k3 + 2k4 + -2k4

Combine like terms: -1k2 + k2 = 0
6k + 8kx2 + 9k2 + -2k3 + -2k4 + 3x2 + 2x4 = 0 + 2k3 + -2k3 + 2k4 + -2k4
6k + 8kx2 + 9k2 + -2k3 + -2k4 + 3x2 + 2x4 = 2k3 + -2k3 + 2k4 + -2k4

Combine like terms: 2k3 + -2k3 = 0
6k + 8kx2 + 9k2 + -2k3 + -2k4 + 3x2 + 2x4 = 0 + 2k4 + -2k4
6k + 8kx2 + 9k2 + -2k3 + -2k4 + 3x2 + 2x4 = 2k4 + -2k4

Combine like terms: 2k4 + -2k4 = 0
6k + 8kx2 + 9k2 + -2k3 + -2k4 + 3x2 + 2x4 = 0

The solution to this equation could not be determined.

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