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

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

Simplifying
(k + -1) * x2 + -1(k + 1) * x + k = 0

Reorder the terms:
(-1 + k) * x2 + -1(k + 1) * x + k = 0

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

Reorder the terms:
(kx2 + -1x2) + -1(k + 1) * x + k = 0
(kx2 + -1x2) + -1(k + 1) * x + k = 0

Reorder the terms:
kx2 + -1x2 + -1(1 + k) * x + k = 0

Reorder the terms for easier multiplication:
kx2 + -1x2 + -1x(1 + k) + k = 0
kx2 + -1x2 + (1 * -1x + k * -1x) + k = 0

Reorder the terms:
kx2 + -1x2 + (-1kx + -1x) + k = 0
kx2 + -1x2 + (-1kx + -1x) + k = 0

Reorder the terms:
k + -1kx + kx2 + -1x + -1x2 = 0

Solving
k + -1kx + kx2 + -1x + -1x2 = 0

Solving for variable 'k'.

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

Add 'x' to each side of the equation.
k + -1kx + kx2 + -1x + x + -1x2 = 0 + x

Combine like terms: -1x + x = 0
k + -1kx + kx2 + 0 + -1x2 = 0 + x
k + -1kx + kx2 + -1x2 = 0 + x
Remove the zero:
k + -1kx + kx2 + -1x2 = x

Add 'x2' to each side of the equation.
k + -1kx + kx2 + -1x2 + x2 = x + x2

Combine like terms: -1x2 + x2 = 0
k + -1kx + kx2 + 0 = x + x2
k + -1kx + kx2 = x + x2

Reorder the terms:
k + -1kx + kx2 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
k + -1kx + kx2 + -1x + -1x2 = 0 + x2 + -1x2
k + -1kx + kx2 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
k + -1kx + kx2 + -1x + -1x2 = 0

The solution to this equation could not be determined.