z^3+x^2=z+1

Solution for z^3+x^2=z+1 equation:

Simplifying
z3 + x2 = z + 1

Reorder the terms:
x2 + z3 = z + 1

Reorder the terms:
x2 + z3 = 1 + z

Solving
x2 + z3 = 1 + z

Solving for variable 'x'.

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

Add '-1z3' to each side of the equation.
x2 + z3 + -1z3 = 1 + z + -1z3

Combine like terms: z3 + -1z3 = 0
x2 + 0 = 1 + z + -1z3
x2 = 1 + z + -1z3

Simplifying
x2 = 1 + z + -1z3

Reorder the terms:
-1 + x2 + -1z + z3 = 1 + z + -1z3 + -1 + -1z + z3

Reorder the terms:
-1 + x2 + -1z + z3 = 1 + -1 + z + -1z + -1z3 + z3

Combine like terms: 1 + -1 = 0
-1 + x2 + -1z + z3 = 0 + z + -1z + -1z3 + z3
-1 + x2 + -1z + z3 = z + -1z + -1z3 + z3

Combine like terms: z + -1z = 0
-1 + x2 + -1z + z3 = 0 + -1z3 + z3
-1 + x2 + -1z + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
-1 + x2 + -1z + z3 = 0

The solution to this equation could not be determined.