(2k+1)x^2+4(k-1)x+k=0

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Solution for (2k+1)x^2+4(k-1)x+k=0 equation: 


Simplifying
(2k + 1) * x2 + 4(k + -1) * x + k = 0

Reorder the terms:
(1 + 2k) * x2 + 4(k + -1) * x + k = 0

Reorder the terms for easier multiplication:
x2(1 + 2k) + 4(k + -1) * x + k = 0
(1 * x2 + 2k * x2) + 4(k + -1) * x + k = 0

Reorder the terms:
(2kx2 + 1x2) + 4(k + -1) * x + k = 0
(2kx2 + 1x2) + 4(k + -1) * x + k = 0

Reorder the terms:
2kx2 + 1x2 + 4(-1 + k) * x + k = 0

Reorder the terms for easier multiplication:
2kx2 + 1x2 + 4x(-1 + k) + k = 0
2kx2 + 1x2 + (-1 * 4x + k * 4x) + k = 0

Reorder the terms:
2kx2 + 1x2 + (4kx + -4x) + k = 0
2kx2 + 1x2 + (4kx + -4x) + k = 0

Reorder the terms:
k + 4kx + 2kx2 + -4x + 1x2 = 0

Solving
k + 4kx + 2kx2 + -4x + 1x2 = 0

Solving for variable 'k'.

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

Add '4x' to each side of the equation.
k + 4kx + 2kx2 + -4x + 4x + 1x2 = 0 + 4x

Combine like terms: -4x + 4x = 0
k + 4kx + 2kx2 + 0 + 1x2 = 0 + 4x
k + 4kx + 2kx2 + 1x2 = 0 + 4x
Remove the zero:
k + 4kx + 2kx2 + 1x2 = 4x

Add '-1x2' to each side of the equation.
k + 4kx + 2kx2 + 1x2 + -1x2 = 4x + -1x2

Combine like terms: 1x2 + -1x2 = 0
k + 4kx + 2kx2 + 0 = 4x + -1x2
k + 4kx + 2kx2 = 4x + -1x2

Reorder the terms:
k + 4kx + 2kx2 + -4x + x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
k + 4kx + 2kx2 + -4x + x2 = 0 + -1x2 + x2
k + 4kx + 2kx2 + -4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
k + 4kx + 2kx2 + -4x + x2 = 0

The solution to this equation could not be determined.

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