(K+1)x^2-2(3k+1)x+8k+1=0

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Solution for (K+1)x^2-2(3k+1)x+8k+1=0 equation: 


Simplifying
(K + 1) * x2 + -2(3k + 1) * x + 8k + 1 = 0

Reorder the terms:
(1 + K) * x2 + -2(3k + 1) * x + 8k + 1 = 0

Reorder the terms for easier multiplication:
x2(1 + K) + -2(3k + 1) * x + 8k + 1 = 0
(1 * x2 + K * x2) + -2(3k + 1) * x + 8k + 1 = 0
(1x2 + x2K) + -2(3k + 1) * x + 8k + 1 = 0

Reorder the terms:
1x2 + x2K + -2(1 + 3k) * x + 8k + 1 = 0

Reorder the terms for easier multiplication:
1x2 + x2K + -2x(1 + 3k) + 8k + 1 = 0
1x2 + x2K + (1 * -2x + 3k * -2x) + 8k + 1 = 0

Reorder the terms:
1x2 + x2K + (-6kx + -2x) + 8k + 1 = 0
1x2 + x2K + (-6kx + -2x) + 8k + 1 = 0

Reorder the terms:
1 + 8k + -6kx + -2x + 1x2 + x2K = 0

Solving
1 + 8k + -6kx + -2x + 1x2 + x2K = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + 8k + -6kx + -2x + 1x2 + -1 + x2K = 0 + -1

Reorder the terms:
1 + -1 + 8k + -6kx + -2x + 1x2 + x2K = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8k + -6kx + -2x + 1x2 + x2K = 0 + -1
8k + -6kx + -2x + 1x2 + x2K = 0 + -1

Combine like terms: 0 + -1 = -1
8k + -6kx + -2x + 1x2 + x2K = -1

Add '2x' to each side of the equation.
8k + -6kx + -2x + 1x2 + 2x + x2K = -1 + 2x

Reorder the terms:
8k + -6kx + -2x + 2x + 1x2 + x2K = -1 + 2x

Combine like terms: -2x + 2x = 0
8k + -6kx + 0 + 1x2 + x2K = -1 + 2x
8k + -6kx + 1x2 + x2K = -1 + 2x

Add '-1x2' to each side of the equation.
8k + -6kx + 1x2 + -1x2 + x2K = -1 + 2x + -1x2

Combine like terms: 1x2 + -1x2 = 0
8k + -6kx + 0 + x2K = -1 + 2x + -1x2
8k + -6kx + x2K = -1 + 2x + -1x2

Add '-1x2K' to each side of the equation.
8k + -6kx + x2K + -1x2K = -1 + 2x + -1x2 + -1x2K

Combine like terms: x2K + -1x2K = 0
8k + -6kx + 0 = -1 + 2x + -1x2 + -1x2K
8k + -6kx = -1 + 2x + -1x2 + -1x2K

Reorder the terms:
1 + 8k + -6kx + -2x + x2 + x2K = -1 + 2x + -1x2 + -1x2K + 1 + -2x + x2 + x2K

Reorder the terms:
1 + 8k + -6kx + -2x + x2 + x2K = -1 + 1 + 2x + -2x + -1x2 + x2 + -1x2K + x2K

Combine like terms: -1 + 1 = 0
1 + 8k + -6kx + -2x + x2 + x2K = 0 + 2x + -2x + -1x2 + x2 + -1x2K + x2K
1 + 8k + -6kx + -2x + x2 + x2K = 2x + -2x + -1x2 + x2 + -1x2K + x2K

Combine like terms: 2x + -2x = 0
1 + 8k + -6kx + -2x + x2 + x2K = 0 + -1x2 + x2 + -1x2K + x2K
1 + 8k + -6kx + -2x + x2 + x2K = -1x2 + x2 + -1x2K + x2K

Combine like terms: -1x2 + x2 = 0
1 + 8k + -6kx + -2x + x2 + x2K = 0 + -1x2K + x2K
1 + 8k + -6kx + -2x + x2 + x2K = -1x2K + x2K

Combine like terms: -1x2K + x2K = 0
1 + 8k + -6kx + -2x + x2 + x2K = 0

The solution to this equation could not be determined.

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