x^3+(k^2-1)x^2+(3k-1)x=0

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Solution for x^3+(k^2-1)x^2+(3k-1)x=0 equation: 


Simplifying
x3 + (k2 + -1) * x2 + (3k + -1) * x = 0

Reorder the terms:
x3 + (-1 + k2) * x2 + (3k + -1) * x = 0

Reorder the terms for easier multiplication:
x3 + x2(-1 + k2) + (3k + -1) * x = 0
x3 + (-1 * x2 + k2 * x2) + (3k + -1) * x = 0

Reorder the terms:
x3 + (k2x2 + -1x2) + (3k + -1) * x = 0
x3 + (k2x2 + -1x2) + (3k + -1) * x = 0

Reorder the terms:
x3 + k2x2 + -1x2 + (-1 + 3k) * x = 0

Reorder the terms for easier multiplication:
x3 + k2x2 + -1x2 + x(-1 + 3k) = 0
x3 + k2x2 + -1x2 + (-1 * x + 3k * x) = 0

Reorder the terms:
x3 + k2x2 + -1x2 + (3kx + -1x) = 0
x3 + k2x2 + -1x2 + (3kx + -1x) = 0

Reorder the terms:
3kx + k2x2 + -1x + -1x2 + x3 = 0

Solving
3kx + k2x2 + -1x + -1x2 + x3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3k + k2x + -1 + -1x + x2) = 0


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

Simplifying
x = 0

Solving
x = 0

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

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

Simplifying
0 = -1x

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 '(3k + k2x + -1 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
3k + k2x + -1 + -1x + x2 = 0

Reorder the terms:
-1 + 3k + k2x + -1x + x2 = 0

Solving
-1 + 3k + k2x + -1x + x2 = 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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