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

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


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

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

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

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

Solving
0 = 1 + 2k + -1kx + -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 + -1kx + -1x + -2k + x2
Remove the zero:
-2k = 1 + 2k + -1kx + -1x + -2k + x2

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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