(-4k^4+14+3k^2)+(-3k^4-14k^2-8)=0

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Solution for (-4k^4+14+3k^2)+(-3k^4-14k^2-8)=0 equation: 


Simplifying
(-4k4 + 14 + 3k2) + (-3k4 + -14k2 + -8) = 0

Reorder the terms:
(14 + 3k2 + -4k4) + (-3k4 + -14k2 + -8) = 0

Remove parenthesis around (14 + 3k2 + -4k4)
14 + 3k2 + -4k4 + (-3k4 + -14k2 + -8) = 0

Reorder the terms:
14 + 3k2 + -4k4 + (-8 + -14k2 + -3k4) = 0

Remove parenthesis around (-8 + -14k2 + -3k4)
14 + 3k2 + -4k4 + -8 + -14k2 + -3k4 = 0

Reorder the terms:
14 + -8 + 3k2 + -14k2 + -4k4 + -3k4 = 0

Combine like terms: 14 + -8 = 6
6 + 3k2 + -14k2 + -4k4 + -3k4 = 0

Combine like terms: 3k2 + -14k2 = -11k2
6 + -11k2 + -4k4 + -3k4 = 0

Combine like terms: -4k4 + -3k4 = -7k4
6 + -11k2 + -7k4 = 0

Solving
6 + -11k2 + -7k4 = 0

Solving for variable 'k'.

Factor a trinomial.
(3 + -7k2)(2 + k2) = 0


Subproblem 1
Set the factor '(3 + -7k2)' equal to zero and attempt to solve:

Simplifying
3 + -7k2 = 0

Solving
3 + -7k2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7k2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7k2 = 0 + -3
-7k2 = 0 + -3

Combine like terms: 0 + -3 = -3
-7k2 = -3

Divide each side by '-7'.
k2 = 0.4285714286

Simplifying
k2 = 0.4285714286

Take the square root of each side:
k = {-0.654653671, 0.654653671}

Subproblem 2
Set the factor '(2 + k2)' equal to zero and attempt to solve:

Simplifying
2 + k2 = 0

Solving
2 + k2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + k2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + k2 = 0 + -2
k2 = 0 + -2

Combine like terms: 0 + -2 = -2
k2 = -2

Simplifying
k2 = -2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
k = {-0.654653671, 0.654653671}

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