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

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


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

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

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

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

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

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

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

Combine like terms: 4x + 8x = 12x
(8 + 12x + 4x2 + 2x2 + x3) = x3 + 8

Combine like terms: 4x2 + 2x2 = 6x2
(8 + 12x + 6x2 + x3) = x3 + 8

Reorder the terms:
8 + 12x + 6x2 + x3 = 8 + x3

Add '-8' to each side of the equation.
8 + 12x + 6x2 + -8 + x3 = 8 + -8 + x3

Reorder the terms:
8 + -8 + 12x + 6x2 + x3 = 8 + -8 + x3

Combine like terms: 8 + -8 = 0
0 + 12x + 6x2 + x3 = 8 + -8 + x3
12x + 6x2 + x3 = 8 + -8 + x3

Combine like terms: 8 + -8 = 0
12x + 6x2 + x3 = 0 + x3
12x + 6x2 + x3 = x3

Add '-1x3' to each side of the equation.
12x + 6x2 + x3 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
12x + 6x2 + 0 = x3 + -1x3
12x + 6x2 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
12x + 6x2 = 0

Solving
12x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(2 + x) = 0

Ignore the factor 6.

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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {0, -2}

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