1-k^4x^4=0

Solution for 1-k^4x^4=0 equation:

Simplifying
1 + -1k4x4 = 0

Solving
1 + -1k4x4 = 0

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + -1k4x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1k4x4 = 0 + -1
-1k4x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-1k4x4 = -1

Divide each side by '-1x4'.
k4 = x-4

Simplifying
k4 = x-4

Combine like terms: x-4 + -1x-4 = 0
k4 + -1x-4 = 0

Factor out the Greatest Common Factor (GCF), 'x-4'.
x-4(k4x4 + -1) = 0

Factor a difference between two squares.
x-4((k2x2 + 1)(k2x2 + -1)) = 0

Factor a difference between two squares.
x-4((k2x2 + 1)((kx + 1)(kx + -1))) = 0

Subproblem 1
Set the factor 'x-4' equal to zero and attempt to solve:

Simplifying
x-4 = 0

Solving
x-4 = 0

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

Add '-1x-4' to each side of the equation.
x-4 + -1x-4 = 0 + -1x-4
Remove the zero:
0 = -1x-4

Simplifying
0 = -1x-4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(k2x2 + 1)' equal to zero and attempt to solve:

Simplifying
k2x2 + 1 = 0

Reorder the terms:
1 + k2x2 = 0

Solving
1 + k2x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + k2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + k2x2 = 0 + -1
k2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
k2x2 = -1

Divide each side by 'x2'.
k2 = -1x-2

Simplifying
k2 = -1x-2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(kx + 1)' equal to zero and attempt to solve:

Simplifying
kx + 1 = 0

Reorder the terms:
1 + kx = 0

Solving
1 + kx = 0

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

Add '-1' to each side of the equation.
1 + -1 + kx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + kx = 0 + -1
kx = 0 + -1

Combine like terms: 0 + -1 = -1
kx = -1

Divide each side by 'x'.
k = -1x-1

Simplifying
k = -1x-1
Subproblem 4
Set the factor '(kx + -1)' equal to zero and attempt to solve:

Simplifying
kx + -1 = 0

Reorder the terms:
-1 + kx = 0

Solving
-1 + kx = 0

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

Add '1' to each side of the equation.
-1 + 1 + kx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + kx = 0 + 1
kx = 0 + 1

Combine like terms: 0 + 1 = 1
kx = 1

Divide each side by 'x'.
k = x-1

Simplifying
k = x-1
Solution
k = {-1x-1, x-1}