(2k-3)x^2-(4k+1)x+(5k+8)=0

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Solution for (2k-3)x^2-(4k+1)x+(5k+8)=0 equation: 


Simplifying
(2k + -3) * x2 + -1(4k + 1) * x + (5k + 8) = 0

Reorder the terms:
(-3 + 2k) * x2 + -1(4k + 1) * x + (5k + 8) = 0

Reorder the terms for easier multiplication:
x2(-3 + 2k) + -1(4k + 1) * x + (5k + 8) = 0
(-3 * x2 + 2k * x2) + -1(4k + 1) * x + (5k + 8) = 0

Reorder the terms:
(2kx2 + -3x2) + -1(4k + 1) * x + (5k + 8) = 0
(2kx2 + -3x2) + -1(4k + 1) * x + (5k + 8) = 0

Reorder the terms:
2kx2 + -3x2 + -1(1 + 4k) * x + (5k + 8) = 0

Reorder the terms for easier multiplication:
2kx2 + -3x2 + -1x(1 + 4k) + (5k + 8) = 0
2kx2 + -3x2 + (1 * -1x + 4k * -1x) + (5k + 8) = 0

Reorder the terms:
2kx2 + -3x2 + (-4kx + -1x) + (5k + 8) = 0
2kx2 + -3x2 + (-4kx + -1x) + (5k + 8) = 0

Reorder the terms:
2kx2 + -3x2 + -4kx + -1x + (8 + 5k) = 0

Remove parenthesis around (8 + 5k)
2kx2 + -3x2 + -4kx + -1x + 8 + 5k = 0

Reorder the terms:
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = 0

Solving
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = 0

Solving for variable 'k'.

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

Add '-8' to each side of the equation.
8 + 5k + -4kx + 2kx2 + -1x + -8 + -3x2 = 0 + -8

Reorder the terms:
8 + -8 + 5k + -4kx + 2kx2 + -1x + -3x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5k + -4kx + 2kx2 + -1x + -3x2 = 0 + -8
5k + -4kx + 2kx2 + -1x + -3x2 = 0 + -8

Combine like terms: 0 + -8 = -8
5k + -4kx + 2kx2 + -1x + -3x2 = -8

Add 'x' to each side of the equation.
5k + -4kx + 2kx2 + -1x + x + -3x2 = -8 + x

Combine like terms: -1x + x = 0
5k + -4kx + 2kx2 + 0 + -3x2 = -8 + x
5k + -4kx + 2kx2 + -3x2 = -8 + x

Add '3x2' to each side of the equation.
5k + -4kx + 2kx2 + -3x2 + 3x2 = -8 + x + 3x2

Combine like terms: -3x2 + 3x2 = 0
5k + -4kx + 2kx2 + 0 = -8 + x + 3x2
5k + -4kx + 2kx2 = -8 + x + 3x2

Reorder the terms:
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = -8 + x + 3x2 + 8 + -1x + -3x2

Reorder the terms:
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = -8 + 8 + x + -1x + 3x2 + -3x2

Combine like terms: -8 + 8 = 0
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = 0 + x + -1x + 3x2 + -3x2
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = x + -1x + 3x2 + -3x2

Combine like terms: x + -1x = 0
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = 0 + 3x2 + -3x2
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
8 + 5k + -4kx + 2kx2 + -1x + -3x2 = 0

The solution to this equation could not be determined.

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