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

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


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

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

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

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

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

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

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

Solving
5 + k + 3kx + -6x + x2 = 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 + 3kx + -6x + -5 + x2 = 0 + -5

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

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

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

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

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

Add '-1x2' to each side of the equation.
k + 3kx + x2 + -1x2 = -5 + 6x + -1x2

Combine like terms: x2 + -1x2 = 0
k + 3kx + 0 = -5 + 6x + -1x2
k + 3kx = -5 + 6x + -1x2

Reorder the terms:
5 + k + 3kx + -6x + x2 = -5 + 6x + -1x2 + 5 + -6x + x2

Reorder the terms:
5 + k + 3kx + -6x + x2 = -5 + 5 + 6x + -6x + -1x2 + x2

Combine like terms: -5 + 5 = 0
5 + k + 3kx + -6x + x2 = 0 + 6x + -6x + -1x2 + x2
5 + k + 3kx + -6x + x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
5 + k + 3kx + -6x + x2 = 0 + -1x2 + x2
5 + k + 3kx + -6x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
5 + k + 3kx + -6x + x2 = 0

The solution to this equation could not be determined.

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