(2k+3)x^2+2(k+3)x+(k+5)=0

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Solution for (2k+3)x^2+2(k+3)x+(k+5)=0 equation: 


Simplifying
(2k + 3) * x2 + 2(k + 3) * x + (k + 5) = 0

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

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

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

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

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

Reorder the terms:
2kx2 + 3x2 + (2kx + 6x) + (k + 5) = 0
2kx2 + 3x2 + (2kx + 6x) + (k + 5) = 0

Reorder the terms:
2kx2 + 3x2 + 2kx + 6x + (5 + k) = 0

Remove parenthesis around (5 + k)
2kx2 + 3x2 + 2kx + 6x + 5 + k = 0

Reorder the terms:
5 + k + 2kx + 2kx2 + 6x + 3x2 = 0

Solving
5 + k + 2kx + 2kx2 + 6x + 3x2 = 0

Solving for variable 'k'.

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

Add '-5' to each side of the equation.
5 + k + 2kx + 2kx2 + 6x + -5 + 3x2 = 0 + -5

Reorder the terms:
5 + -5 + k + 2kx + 2kx2 + 6x + 3x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + k + 2kx + 2kx2 + 6x + 3x2 = 0 + -5
k + 2kx + 2kx2 + 6x + 3x2 = 0 + -5

Combine like terms: 0 + -5 = -5
k + 2kx + 2kx2 + 6x + 3x2 = -5

Add '-6x' to each side of the equation.
k + 2kx + 2kx2 + 6x + -6x + 3x2 = -5 + -6x

Combine like terms: 6x + -6x = 0
k + 2kx + 2kx2 + 0 + 3x2 = -5 + -6x
k + 2kx + 2kx2 + 3x2 = -5 + -6x

Add '-3x2' to each side of the equation.
k + 2kx + 2kx2 + 3x2 + -3x2 = -5 + -6x + -3x2

Combine like terms: 3x2 + -3x2 = 0
k + 2kx + 2kx2 + 0 = -5 + -6x + -3x2
k + 2kx + 2kx2 = -5 + -6x + -3x2

Reorder the terms:
5 + k + 2kx + 2kx2 + 6x + 3x2 = -5 + -6x + -3x2 + 5 + 6x + 3x2

Reorder the terms:
5 + k + 2kx + 2kx2 + 6x + 3x2 = -5 + 5 + -6x + 6x + -3x2 + 3x2

Combine like terms: -5 + 5 = 0
5 + k + 2kx + 2kx2 + 6x + 3x2 = 0 + -6x + 6x + -3x2 + 3x2
5 + k + 2kx + 2kx2 + 6x + 3x2 = -6x + 6x + -3x2 + 3x2

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

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

The solution to this equation could not be determined.

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