(2x-k)(3x-2k)=6x^2+kx-32

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Solution for (2x-k)(3x-2k)=6x^2+kx-32 equation: 


Simplifying
(2x + -1k)(3x + -2k) = 6x2 + kx + -32

Reorder the terms:
(-1k + 2x)(3x + -2k) = 6x2 + kx + -32

Reorder the terms:
(-1k + 2x)(-2k + 3x) = 6x2 + kx + -32

Multiply (-1k + 2x) * (-2k + 3x)
(-1k * (-2k + 3x) + 2x * (-2k + 3x)) = 6x2 + kx + -32
((-2k * -1k + 3x * -1k) + 2x * (-2k + 3x)) = 6x2 + kx + -32

Reorder the terms:
((-3kx + 2k2) + 2x * (-2k + 3x)) = 6x2 + kx + -32
((-3kx + 2k2) + 2x * (-2k + 3x)) = 6x2 + kx + -32
(-3kx + 2k2 + (-2k * 2x + 3x * 2x)) = 6x2 + kx + -32
(-3kx + 2k2 + (-4kx + 6x2)) = 6x2 + kx + -32

Reorder the terms:
(-3kx + -4kx + 2k2 + 6x2) = 6x2 + kx + -32

Combine like terms: -3kx + -4kx = -7kx
(-7kx + 2k2 + 6x2) = 6x2 + kx + -32

Reorder the terms:
-7kx + 2k2 + 6x2 = -32 + kx + 6x2

Add '-6x2' to each side of the equation.
-7kx + 2k2 + 6x2 + -6x2 = -32 + kx + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-7kx + 2k2 + 0 = -32 + kx + 6x2 + -6x2
-7kx + 2k2 = -32 + kx + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-7kx + 2k2 = -32 + kx + 0
-7kx + 2k2 = -32 + kx

Solving
-7kx + 2k2 = -32 + kx

Solving for variable 'k'.

Reorder the terms:
32 + -7kx + -1kx + 2k2 = -32 + kx + 32 + -1kx

Combine like terms: -7kx + -1kx = -8kx
32 + -8kx + 2k2 = -32 + kx + 32 + -1kx

Reorder the terms:
32 + -8kx + 2k2 = -32 + 32 + kx + -1kx

Combine like terms: -32 + 32 = 0
32 + -8kx + 2k2 = 0 + kx + -1kx
32 + -8kx + 2k2 = kx + -1kx

Combine like terms: kx + -1kx = 0
32 + -8kx + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -4kx + k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -4kx + k2)' equal to zero and attempt to solve:

Simplifying
16 + -4kx + k2 = 0

Solving
16 + -4kx + k2 = 0

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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