(12k^7+4k^5-k^2)(2k^2-3)=0

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Solution for (12k^7+4k^5-k^2)(2k^2-3)=0 equation: 


Simplifying
(12k7 + 4k5 + -1k2)(2k2 + -3) = 0

Reorder the terms:
(-1k2 + 4k5 + 12k7)(2k2 + -3) = 0

Reorder the terms:
(-1k2 + 4k5 + 12k7)(-3 + 2k2) = 0

Multiply (-1k2 + 4k5 + 12k7) * (-3 + 2k2)
(-1k2 * (-3 + 2k2) + 4k5 * (-3 + 2k2) + 12k7 * (-3 + 2k2)) = 0
((-3 * -1k2 + 2k2 * -1k2) + 4k5 * (-3 + 2k2) + 12k7 * (-3 + 2k2)) = 0
((3k2 + -2k4) + 4k5 * (-3 + 2k2) + 12k7 * (-3 + 2k2)) = 0
(3k2 + -2k4 + (-3 * 4k5 + 2k2 * 4k5) + 12k7 * (-3 + 2k2)) = 0
(3k2 + -2k4 + (-12k5 + 8k7) + 12k7 * (-3 + 2k2)) = 0
(3k2 + -2k4 + -12k5 + 8k7 + (-3 * 12k7 + 2k2 * 12k7)) = 0
(3k2 + -2k4 + -12k5 + 8k7 + (-36k7 + 24k9)) = 0

Combine like terms: 8k7 + -36k7 = -28k7
(3k2 + -2k4 + -12k5 + -28k7 + 24k9) = 0

Solving
3k2 + -2k4 + -12k5 + -28k7 + 24k9 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k2'.
k2(3 + -2k2 + -12k3 + -28k5 + 24k7) = 0


Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve:

Simplifying
k2 = 0

Solving
k2 = 0

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

Simplifying
k2 = 0

Take the square root of each side:
k = {0}

Subproblem 2
Set the factor '(3 + -2k2 + -12k3 + -28k5 + 24k7)' equal to zero and attempt to solve:

Simplifying
3 + -2k2 + -12k3 + -28k5 + 24k7 = 0

Solving
3 + -2k2 + -12k3 + -28k5 + 24k7 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
k = {0}

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