(6k^2+2k^4)-(k^3+k^4-4k^2)=

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Solution for (6k^2+2k^4)-(k^3+k^4-4k^2)= equation: 


Simplifying
(6k2 + 2k4) + -1(k3 + k4 + -4k2) = 0

Remove parenthesis around (6k2 + 2k4)
6k2 + 2k4 + -1(k3 + k4 + -4k2) = 0

Reorder the terms:
6k2 + 2k4 + -1(-4k2 + k3 + k4) = 0
6k2 + 2k4 + (-4k2 * -1 + k3 * -1 + k4 * -1) = 0
6k2 + 2k4 + (4k2 + -1k3 + -1k4) = 0

Reorder the terms:
6k2 + 4k2 + -1k3 + 2k4 + -1k4 = 0

Combine like terms: 6k2 + 4k2 = 10k2
10k2 + -1k3 + 2k4 + -1k4 = 0

Combine like terms: 2k4 + -1k4 = 1k4
10k2 + -1k3 + 1k4 = 0

Solving
10k2 + -1k3 + 1k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k2'.
k2(10 + -1k + k2) = 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 '(10 + -1k + k2)' equal to zero and attempt to solve:

Simplifying
10 + -1k + k2 = 0

Solving
10 + -1k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -1k + -10 + k2 = 0 + -10

Reorder the terms:
10 + -10 + -1k + k2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1k + k2 = 0 + -10
-1k + k2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1k + k2 = -10

The k term is -1k.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1k + 0.25 + k2 = -10 + 0.25

Reorder the terms:
0.25 + -1k + k2 = -10 + 0.25

Combine like terms: -10 + 0.25 = -9.75
0.25 + -1k + k2 = -9.75

Factor a perfect square on the left side:
(k + -0.5)(k + -0.5) = -9.75

Can't calculate square root of the right side.

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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