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

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


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

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

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

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

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

Reorder the terms:
-2 + 4k + 3kx + 2x + x2 = 0

Solving
-2 + 4k + 3kx + 2x + x2 = 0

Solving for variable 'k'.

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

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

Reorder the terms:
-2 + 2 + 4k + 3kx + 2x + x2 = 0 + 2

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

Combine like terms: 0 + 2 = 2
4k + 3kx + 2x + x2 = 2

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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