x^3+2(x+3)=3x+6

Solution for x^3+2(x+3)=3x+6 equation:

Simplifying
x3 + 2(x + 3) = 3x + 6

Reorder the terms:
x3 + 2(3 + x) = 3x + 6
x3 + (3 * 2 + x * 2) = 3x + 6
x3 + (6 + 2x) = 3x + 6

Reorder the terms:
6 + 2x + x3 = 3x + 6

Reorder the terms:
6 + 2x + x3 = 6 + 3x

Add '-6' to each side of the equation.
6 + 2x + -6 + x3 = 6 + -6 + 3x

Reorder the terms:
6 + -6 + 2x + x3 = 6 + -6 + 3x

Combine like terms: 6 + -6 = 0
0 + 2x + x3 = 6 + -6 + 3x
2x + x3 = 6 + -6 + 3x

Combine like terms: 6 + -6 = 0
2x + x3 = 0 + 3x
2x + x3 = 3x

Solving
2x + x3 = 3x

Solving for variable 'x'.

Reorder the terms:
2x + -3x + x3 = 3x + -3x

Combine like terms: 2x + -3x = -1x
-1x + x3 = 3x + -3x

Combine like terms: 3x + -3x = 0
-1x + x3 = 0

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

Factor a difference between two squares.
x((1 + x)(-1 + x)) = 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 3
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

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