x(x+1)(x+2)=x^3+208

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Solution for x(x+1)(x+2)=x^3+208 equation: 


Simplifying
x(x + 1)(x + 2) = x3 + 208

Reorder the terms:
x(1 + x)(x + 2) = x3 + 208

Reorder the terms:
x(1 + x)(2 + x) = x3 + 208

Multiply (1 + x) * (2 + x)
x(1(2 + x) + x(2 + x)) = x3 + 208
x((2 * 1 + x * 1) + x(2 + x)) = x3 + 208
x((2 + 1x) + x(2 + x)) = x3 + 208
x(2 + 1x + (2 * x + x * x)) = x3 + 208
x(2 + 1x + (2x + x2)) = x3 + 208

Combine like terms: 1x + 2x = 3x
x(2 + 3x + x2) = x3 + 208
(2 * x + 3x * x + x2 * x) = x3 + 208
(2x + 3x2 + x3) = x3 + 208

Reorder the terms:
2x + 3x2 + x3 = 208 + x3

Add '-1x3' to each side of the equation.
2x + 3x2 + x3 + -1x3 = 208 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2x + 3x2 + 0 = 208 + x3 + -1x3
2x + 3x2 = 208 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2x + 3x2 = 208 + 0
2x + 3x2 = 208

Solving
2x + 3x2 = 208

Solving for variable 'x'.

Reorder the terms:
-208 + 2x + 3x2 = 208 + -208

Combine like terms: 208 + -208 = 0
-208 + 2x + 3x2 = 0

Factor a trinomial.
(-26 + -3x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-26 + -3x)' equal to zero and attempt to solve:

Simplifying
-26 + -3x = 0

Solving
-26 + -3x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -3x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -3x = 0 + 26
-3x = 0 + 26

Combine like terms: 0 + 26 = 26
-3x = 26

Divide each side by '-3'.
x = -8.666666667

Simplifying
x = -8.666666667

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-8.666666667, 8}

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