x(x+1)(x+2)=33+x^3

Solution for x(x+1)(x+2)=33+x^3 equation:

Simplifying
x(x + 1)(x + 2) = 33 + x3

Reorder the terms:
x(1 + x)(x + 2) = 33 + x3

Reorder the terms:
x(1 + x)(2 + x) = 33 + x3

Multiply (1 + x) * (2 + x)
x(1(2 + x) + x(2 + x)) = 33 + x3
x((2 * 1 + x * 1) + x(2 + x)) = 33 + x3
x((2 + 1x) + x(2 + x)) = 33 + x3
x(2 + 1x + (2 * x + x * x)) = 33 + x3
x(2 + 1x + (2x + x2)) = 33 + x3

Combine like terms: 1x + 2x = 3x
x(2 + 3x + x2) = 33 + x3
(2 * x + 3x * x + x2 * x) = 33 + x3
(2x + 3x2 + x3) = 33 + x3

Add '-1x3' to each side of the equation.
2x + 3x2 + x3 + -1x3 = 33 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2x + 3x2 + 0 = 33 + x3 + -1x3
2x + 3x2 = 33 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2x + 3x2 = 33 + 0
2x + 3x2 = 33

Solving
2x + 3x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + 2x + 3x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 2x + 3x2 = 0

Factor a trinomial.
(-11 + -3x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.666666667, 3}