0=x^3+2x^2+8x

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Solution for 0=x^3+2x^2+8x equation: 


Simplifying
0 = x3 + 2x2 + 8x

Reorder the terms:
0 = 8x + 2x2 + x3

Solving
0 = 8x + 2x2 + x3

Solving for variable 'x'.
Remove the zero:
-8x + -2x2 + -1x3 = 8x + 2x2 + x3 + -8x + -2x2 + -1x3

Reorder the terms:
-8x + -2x2 + -1x3 = 8x + -8x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: 8x + -8x = 0
-8x + -2x2 + -1x3 = 0 + 2x2 + -2x2 + x3 + -1x3
-8x + -2x2 + -1x3 = 2x2 + -2x2 + x3 + -1x3

Combine like terms: 2x2 + -2x2 = 0
-8x + -2x2 + -1x3 = 0 + x3 + -1x3
-8x + -2x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-8x + -2x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(8 + 2x + x2) = 0

Ignore the factor -1.

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 '(8 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
8 + 2x + x2 = 0

Solving
8 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 2x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 2x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 2x + x2 = 0 + -8
2x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
2x + x2 = -8

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -8 + 1

Reorder the terms:
1 + 2x + x2 = -8 + 1

Combine like terms: -8 + 1 = -7
1 + 2x + x2 = -7

Factor a perfect square on the left side:
(x + 1)(x + 1) = -7

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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