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

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

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

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

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

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

Solving
k + -1x + -1x2 + x2K = 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 + -1x + -1x2 + x + x2K = 0 + x

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

Combine like terms: -1x + x = 0
k + 0 + -1x2 + x2K = 0 + x
k + -1x2 + x2K = 0 + x
Remove the zero:
k + -1x2 + x2K = x

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

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

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

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

Simplifying
k = x + x2 + -1x2K