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

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


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

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

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

Multiply x * x
x2(1 + K) + 2(k + 3) * x + (k + 8) = 0
(1 * x2 + K * x2) + 2(k + 3) * x + (k + 8) = 0
(1x2 + x2K) + 2(k + 3) * x + (k + 8) = 0

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

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

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

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

Remove parenthesis around (8 + k)
1x2 + x2K + 2kx + 6x + 8 + k = 0

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

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

Solving for variable 'k'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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