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

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

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

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

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

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

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

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

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

Solving for variable 'k'.

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

Add '2k' to each side of the equation.
0 + 2k = 1 + -2k + 2kx + 1x + 2k + x2
Remove the zero:
2k = 1 + -2k + 2kx + 1x + 2k + x2

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.