5x^3+8x^2+6x=0

Solution for 5x^3+8x^2+6x=0 equation:

Simplifying
5x3 + 8x2 + 6x = 0

Reorder the terms:
6x + 8x2 + 5x3 = 0

Solving
6x + 8x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + 8x + 5x2) = 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 '(6 + 8x + 5x2)' equal to zero and attempt to solve:

Simplifying
6 + 8x + 5x2 = 0

Solving
6 + 8x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.2 + 1.6x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 1.6x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 1.6x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 1.6x + x2 = 0 + -1.2
1.6x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
1.6x + x2 = -1.2

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = -1.2 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = -1.2 + 0.64

Combine like terms: -1.2 + 0.64 = -0.56
0.64 + 1.6x + x2 = -0.56

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = -0.56

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}