2x+1=x^3+1

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

Simplifying
2x + 1 = x3 + 1

Reorder the terms:
1 + 2x = x3 + 1

Reorder the terms:
1 + 2x = 1 + x3

Add '-1' to each side of the equation.
1 + -1 + 2x = 1 + -1 + x3

Combine like terms: 1 + -1 = 0
0 + 2x = 1 + -1 + x3
2x = 1 + -1 + x3

Combine like terms: 1 + -1 = 0
2x = 0 + x3
2x = x3

Solving
2x = x3

Solving for variable 'x'.

Combine like terms: x3 + -1x3 = 0
2x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + -1x2) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

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

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {0, -1.414213562, 1.414213562}