(2k-3)x^2+2x+(k-1)=0

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Solution for (2k-3)x^2+2x+(k-1)=0 equation: 


Simplifying
(2k + -3) * x2 + 2x + (k + -1) = 0

Reorder the terms:
(-3 + 2k) * x2 + 2x + (k + -1) = 0

Reorder the terms for easier multiplication:
x2(-3 + 2k) + 2x + (k + -1) = 0
(-3 * x2 + 2k * x2) + 2x + (k + -1) = 0

Reorder the terms:
(2kx2 + -3x2) + 2x + (k + -1) = 0
(2kx2 + -3x2) + 2x + (k + -1) = 0

Reorder the terms:
2kx2 + -3x2 + 2x + (-1 + k) = 0

Remove parenthesis around (-1 + k)
2kx2 + -3x2 + 2x + -1 + k = 0

Reorder the terms:
-1 + k + 2kx2 + 2x + -3x2 = 0

Solving
-1 + k + 2kx2 + 2x + -3x2 = 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 + k + 2kx2 + 2x + 1 + -3x2 = 0 + 1

Reorder the terms:
-1 + 1 + k + 2kx2 + 2x + -3x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + k + 2kx2 + 2x + -3x2 = 0 + 1
k + 2kx2 + 2x + -3x2 = 0 + 1

Combine like terms: 0 + 1 = 1
k + 2kx2 + 2x + -3x2 = 1

Add '-2x' to each side of the equation.
k + 2kx2 + 2x + -2x + -3x2 = 1 + -2x

Combine like terms: 2x + -2x = 0
k + 2kx2 + 0 + -3x2 = 1 + -2x
k + 2kx2 + -3x2 = 1 + -2x

Add '3x2' to each side of the equation.
k + 2kx2 + -3x2 + 3x2 = 1 + -2x + 3x2

Combine like terms: -3x2 + 3x2 = 0
k + 2kx2 + 0 = 1 + -2x + 3x2
k + 2kx2 = 1 + -2x + 3x2

Reorder the terms:
-1 + k + 2kx2 + 2x + -3x2 = 1 + -2x + 3x2 + -1 + 2x + -3x2

Reorder the terms:
-1 + k + 2kx2 + 2x + -3x2 = 1 + -1 + -2x + 2x + 3x2 + -3x2

Combine like terms: 1 + -1 = 0
-1 + k + 2kx2 + 2x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2
-1 + k + 2kx2 + 2x + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
-1 + k + 2kx2 + 2x + -3x2 = 0 + 3x2 + -3x2
-1 + k + 2kx2 + 2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-1 + k + 2kx2 + 2x + -3x2 = 0

The solution to this equation could not be determined.

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