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

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


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

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

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

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

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

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

Reorder the terms:
2kx2 + -3x2 + (2kx + -6x) + 1 = 0
2kx2 + -3x2 + (2kx + -6x) + 1 = 0

Reorder the terms:
1 + 2kx + 2kx2 + -6x + -3x2 = 0

Solving
1 + 2kx + 2kx2 + -6x + -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 + 2kx + 2kx2 + -6x + -1 + -3x2 = 0 + -1

Reorder the terms:
1 + -1 + 2kx + 2kx2 + -6x + -3x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2kx + 2kx2 + -6x + -3x2 = 0 + -1
2kx + 2kx2 + -6x + -3x2 = 0 + -1

Combine like terms: 0 + -1 = -1
2kx + 2kx2 + -6x + -3x2 = -1

Add '6x' to each side of the equation.
2kx + 2kx2 + -6x + 6x + -3x2 = -1 + 6x

Combine like terms: -6x + 6x = 0
2kx + 2kx2 + 0 + -3x2 = -1 + 6x
2kx + 2kx2 + -3x2 = -1 + 6x

Add '3x2' to each side of the equation.
2kx + 2kx2 + -3x2 + 3x2 = -1 + 6x + 3x2

Combine like terms: -3x2 + 3x2 = 0
2kx + 2kx2 + 0 = -1 + 6x + 3x2
2kx + 2kx2 = -1 + 6x + 3x2

Reorder the terms:
1 + 2kx + 2kx2 + -6x + -3x2 = -1 + 6x + 3x2 + 1 + -6x + -3x2

Reorder the terms:
1 + 2kx + 2kx2 + -6x + -3x2 = -1 + 1 + 6x + -6x + 3x2 + -3x2

Combine like terms: -1 + 1 = 0
1 + 2kx + 2kx2 + -6x + -3x2 = 0 + 6x + -6x + 3x2 + -3x2
1 + 2kx + 2kx2 + -6x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
1 + 2kx + 2kx2 + -6x + -3x2 = 0 + 3x2 + -3x2
1 + 2kx + 2kx2 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
1 + 2kx + 2kx2 + -6x + -3x2 = 0

The solution to this equation could not be determined.

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