(x+1)(x+2)(x-2)=x^3+8

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Solution for (x+1)(x+2)(x-2)=x^3+8 equation: 


Simplifying
(x + 1)(x + 2)(x + -2) = x3 + 8

Reorder the terms:
(1 + x)(x + 2)(x + -2) = x3 + 8

Reorder the terms:
(1 + x)(2 + x)(x + -2) = x3 + 8

Reorder the terms:
(1 + x)(2 + x)(-2 + x) = x3 + 8

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x))(-2 + x) = x3 + 8
((2 * 1 + x * 1) + x(2 + x))(-2 + x) = x3 + 8
((2 + 1x) + x(2 + x))(-2 + x) = x3 + 8
(2 + 1x + (2 * x + x * x))(-2 + x) = x3 + 8
(2 + 1x + (2x + x2))(-2 + x) = x3 + 8

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2)(-2 + x) = x3 + 8

Multiply (2 + 3x + x2) * (-2 + x)
(2(-2 + x) + 3x * (-2 + x) + x2(-2 + x)) = x3 + 8
((-2 * 2 + x * 2) + 3x * (-2 + x) + x2(-2 + x)) = x3 + 8
((-4 + 2x) + 3x * (-2 + x) + x2(-2 + x)) = x3 + 8
(-4 + 2x + (-2 * 3x + x * 3x) + x2(-2 + x)) = x3 + 8
(-4 + 2x + (-6x + 3x2) + x2(-2 + x)) = x3 + 8
(-4 + 2x + -6x + 3x2 + (-2 * x2 + x * x2)) = x3 + 8
(-4 + 2x + -6x + 3x2 + (-2x2 + x3)) = x3 + 8

Combine like terms: 2x + -6x = -4x
(-4 + -4x + 3x2 + -2x2 + x3) = x3 + 8

Combine like terms: 3x2 + -2x2 = 1x2
(-4 + -4x + 1x2 + x3) = x3 + 8

Reorder the terms:
-4 + -4x + 1x2 + x3 = 8 + x3

Add '-1x3' to each side of the equation.
-4 + -4x + 1x2 + x3 + -1x3 = 8 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-4 + -4x + 1x2 + 0 = 8 + x3 + -1x3
-4 + -4x + 1x2 = 8 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-4 + -4x + 1x2 = 8 + 0
-4 + -4x + 1x2 = 8

Solving
-4 + -4x + 1x2 = 8

Solving for variable 'x'.

Reorder the terms:
-4 + -8 + -4x + 1x2 = 8 + -8

Combine like terms: -4 + -8 = -12
-12 + -4x + 1x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-12 + -4x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}

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