2x^3+5x^2+12x=0

Solution for 2x^3+5x^2+12x=0 equation:

Simplifying
2x3 + 5x2 + 12x = 0

Reorder the terms:
12x + 5x2 + 2x3 = 0

Solving
12x + 5x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + 5x + 2x2) = 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 '(12 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
12 + 5x + 2x2 = 0

Solving
12 + 5x + 2x2 = 0

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

Divide each side by '2'.
6 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 2.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 2.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 2.5x + x2 = 0 + -6
2.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
2.5x + x2 = -6

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -6 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -6 + 1.5625

Combine like terms: -6 + 1.5625 = -4.4375
1.5625 + 2.5x + x2 = -4.4375

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = -4.4375

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}