4x^2+(4k+2)x+4k=0

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Solution for 4x^2+(4k+2)x+4k=0 equation: 


Simplifying
4x2 + (4k + 2) * x + 4k = 0

Reorder the terms:
4x2 + (2 + 4k) * x + 4k = 0

Reorder the terms for easier multiplication:
4x2 + x(2 + 4k) + 4k = 0
4x2 + (2 * x + 4k * x) + 4k = 0

Reorder the terms:
4x2 + (4kx + 2x) + 4k = 0
4x2 + (4kx + 2x) + 4k = 0

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

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

Solving for variable 'k'.

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

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

Combine like terms: 2x + -2x = 0
4k + 4kx + 0 + 4x2 = 0 + -2x
4k + 4kx + 4x2 = 0 + -2x
Remove the zero:
4k + 4kx + 4x2 = -2x

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(2k + 2kx + x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2k + 2kx + x + 2x2)' equal to zero and attempt to solve:

Simplifying
2k + 2kx + x + 2x2 = 0

Solving
2k + 2kx + x + 2x2 = 0

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

Add '-1x' to each side of the equation.
2k + 2kx + x + -1x + 2x2 = 0 + -1x

Combine like terms: x + -1x = 0
2k + 2kx + 0 + 2x2 = 0 + -1x
2k + 2kx + 2x2 = 0 + -1x
Remove the zero:
2k + 2kx + 2x2 = -1x

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

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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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