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

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

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

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

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

Reorder the terms:
(2kx2 + -2x2) + 2kx + -1 = 0
(2kx2 + -2x2) + 2kx + -1 = 0

Reorder the terms:
-1 + 2kx + 2kx2 + -2x2 = 0

Solving
-1 + 2kx + 2kx2 + -2x2 = 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 + 2kx + 2kx2 + 1 + -2x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2kx + 2kx2 + -2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2kx + 2kx2 + -2x2 = 0 + 1
2kx + 2kx2 + -2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2kx + 2kx2 + -2x2 = 1

Add '2x2' to each side of the equation.
2kx + 2kx2 + -2x2 + 2x2 = 1 + 2x2

Combine like terms: -2x2 + 2x2 = 0
2kx + 2kx2 + 0 = 1 + 2x2
2kx + 2kx2 = 1 + 2x2

Reorder the terms:
-1 + 2kx + 2kx2 + -2x2 = 1 + 2x2 + -1 + -2x2

Reorder the terms:
-1 + 2kx + 2kx2 + -2x2 = 1 + -1 + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
-1 + 2kx + 2kx2 + -2x2 = 0 + 2x2 + -2x2
-1 + 2kx + 2kx2 + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1 + 2kx + 2kx2 + -2x2 = 0

The solution to this equation could not be determined.