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

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


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

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

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

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

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

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

Reorder the terms:
(2kx2 + 1x2 + (2kx + 6x)) + (k + 5) = 0
(2kx2 + 1x2 + (2kx + 6x)) + (k + 5) = 0

Reorder the terms:
(2kx + 2kx2 + 6x + 1x2) + (k + 5) = 0

Remove parenthesis around (2kx + 2kx2 + 6x + 1x2)
2kx + 2kx2 + 6x + 1x2 + (k + 5) = 0

Reorder the terms:
2kx + 2kx2 + 6x + 1x2 + (5 + k) = 0

Remove parenthesis around (5 + k)
2kx + 2kx2 + 6x + 1x2 + 5 + k = 0

Reorder the terms:
5 + k + 2kx + 2kx2 + 6x + 1x2 = 0

Solving
5 + k + 2kx + 2kx2 + 6x + 1x2 = 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 + 1x2 = 0 + -5

Reorder the terms:
5 + -5 + k + 2kx + 2kx2 + 6x + 1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + k + 2kx + 2kx2 + 6x + 1x2 = 0 + -5
k + 2kx + 2kx2 + 6x + 1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
k + 2kx + 2kx2 + 6x + 1x2 = -5

Add '-6x' to each side of the equation.
k + 2kx + 2kx2 + 6x + -6x + 1x2 = -5 + -6x

Combine like terms: 6x + -6x = 0
k + 2kx + 2kx2 + 0 + 1x2 = -5 + -6x
k + 2kx + 2kx2 + 1x2 = -5 + -6x

Add '-1x2' to each side of the equation.
k + 2kx + 2kx2 + 1x2 + -1x2 = -5 + -6x + -1x2

Combine like terms: 1x2 + -1x2 = 0
k + 2kx + 2kx2 + 0 = -5 + -6x + -1x2
k + 2kx + 2kx2 = -5 + -6x + -1x2

Reorder the terms:
5 + k + 2kx + 2kx2 + 6x + x2 = -5 + -6x + -1x2 + 5 + 6x + x2

Reorder the terms:
5 + k + 2kx + 2kx2 + 6x + x2 = -5 + 5 + -6x + 6x + -1x2 + x2

Combine like terms: -5 + 5 = 0
5 + k + 2kx + 2kx2 + 6x + x2 = 0 + -6x + 6x + -1x2 + x2
5 + k + 2kx + 2kx2 + 6x + x2 = -6x + 6x + -1x2 + x2

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

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

The solution to this equation could not be determined.

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