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

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


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

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

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

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

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

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

Solving for variable 'k'.

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

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(k + -1kx + -2x + 2x2) = 0

Ignore the factor 2.

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

Simplifying
k + -1kx + -2x + 2x2 = 0

Solving
k + -1kx + -2x + 2x2 = 0

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

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

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

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

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