x^3+6x^2=-8x

Solution for x^3+6x^2=-8x equation:

Simplifying
x3 + 6x2 = -8x

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

Solving
6x2 + x3 = -8x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + 6x + x2) = 0

Factor a trinomial.
x((4 + x)(2 + x)) = 0

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 3
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, -4, -2}