x(x+1)(x+2)=x^3+85

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Solution for x(x+1)(x+2)=x^3+85 equation: 


Simplifying
x(x + 1)(x + 2) = x3 + 85

Reorder the terms:
x(1 + x)(x + 2) = x3 + 85

Reorder the terms:
x(1 + x)(2 + x) = x3 + 85

Multiply (1 + x) * (2 + x)
x(1(2 + x) + x(2 + x)) = x3 + 85
x((2 * 1 + x * 1) + x(2 + x)) = x3 + 85
x((2 + 1x) + x(2 + x)) = x3 + 85
x(2 + 1x + (2 * x + x * x)) = x3 + 85
x(2 + 1x + (2x + x2)) = x3 + 85

Combine like terms: 1x + 2x = 3x
x(2 + 3x + x2) = x3 + 85
(2 * x + 3x * x + x2 * x) = x3 + 85
(2x + 3x2 + x3) = x3 + 85

Reorder the terms:
2x + 3x2 + x3 = 85 + x3

Add '-1x3' to each side of the equation.
2x + 3x2 + x3 + -1x3 = 85 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2x + 3x2 + 0 = 85 + x3 + -1x3
2x + 3x2 = 85 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2x + 3x2 = 85 + 0
2x + 3x2 = 85

Solving
2x + 3x2 = 85

Solving for variable 'x'.

Reorder the terms:
-85 + 2x + 3x2 = 85 + -85

Combine like terms: 85 + -85 = 0
-85 + 2x + 3x2 = 0

Factor a trinomial.
(-17 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-17 + -3x)' equal to zero and attempt to solve:

Simplifying
-17 + -3x = 0

Solving
-17 + -3x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -3x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -3x = 0 + 17
-3x = 0 + 17

Combine like terms: 0 + 17 = 17
-3x = 17

Divide each side by '-3'.
x = -5.666666667

Simplifying
x = -5.666666667

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-5.666666667, 5}

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