1=k^2x-k+1

Solution for 1=k^2x-k+1 equation:

Simplifying
1 = k2x + -1k + 1

Reorder the terms:
1 = 1 + -1k + k2x

Add '-1' to each side of the equation.
1 + -1 = 1 + -1k + -1 + k2x

Combine like terms: 1 + -1 = 0
0 = 1 + -1k + -1 + k2x

Reorder the terms:
0 = 1 + -1 + -1k + k2x

Combine like terms: 1 + -1 = 0
0 = 0 + -1k + k2x
0 = -1k + k2x

Solving
0 = -1k + k2x

Solving for variable 'k'.
Remove the zero:
k + -1k2x = -1k + k2x + k + -1k2x

Reorder the terms:
k + -1k2x = -1k + k + k2x + -1k2x

Combine like terms: -1k + k = 0
k + -1k2x = 0 + k2x + -1k2x
k + -1k2x = k2x + -1k2x

Combine like terms: k2x + -1k2x = 0
k + -1k2x = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(1 + -1kx) = 0

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

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(1 + -1kx)' equal to zero and attempt to solve:

Simplifying
1 + -1kx = 0

Solving
1 + -1kx = 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 + -1kx = 0 + -1

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

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

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

Simplifying
k = x-1
Solution
k = {0, x-1}