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

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


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

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

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

Remove parenthesis around (1 + -1K)
-1x2 + x2K + 2x + 1 + -1K = 0

Reorder the terms:
1 + -1K + 2x + -1x2 + x2K = 0

Solving
1 + -1K + 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 + -1K + 2x + -1x2 + -1 + x2K = 0 + -1

Reorder the terms:
1 + -1 + -1K + 2x + -1x2 + x2K = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1K + 2x + -1x2 + x2K = 0 + -1
-1K + 2x + -1x2 + x2K = 0 + -1

Combine like terms: 0 + -1 = -1
-1K + 2x + -1x2 + x2K = -1

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

Reorder the terms:
-1K + 2x + -2x + -1x2 + x2K = -1 + -2x

Combine like terms: 2x + -2x = 0
-1K + 0 + -1x2 + x2K = -1 + -2x
-1K + -1x2 + x2K = -1 + -2x

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

Combine like terms: -1x2 + x2 = 0
-1K + 0 + x2K = -1 + -2x + x2
-1K + x2K = -1 + -2x + x2

Reorder the terms:
1 + -1K + 2x + -1x2 + x2K = -1 + -2x + x2 + 1 + 2x + -1x2

Reorder the terms:
1 + -1K + 2x + -1x2 + x2K = -1 + 1 + -2x + 2x + x2 + -1x2

Combine like terms: -1 + 1 = 0
1 + -1K + 2x + -1x2 + x2K = 0 + -2x + 2x + x2 + -1x2
1 + -1K + 2x + -1x2 + x2K = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
1 + -1K + 2x + -1x2 + x2K = 0 + x2 + -1x2
1 + -1K + 2x + -1x2 + x2K = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + -1K + 2x + -1x2 + x2K = 0

The solution to this equation could not be determined.

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