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

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

Simplifying
(K + 1) * x2 + 2kx + (k + -1) = 0

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

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

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

Remove parenthesis around (-1 + k)
1x2 + x2K + 2kx + -1 + k = 0

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

Solving
-1 + k + 2kx + 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 + k + 2kx + 1x2 + 1 + x2K = 0 + 1

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

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

Combine like terms: 0 + 1 = 1
k + 2kx + 1x2 + x2K = 1

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.