3x^3+24x^2+61x=0

Solution for 3x^3+24x^2+61x=0 equation:

Simplifying
3x3 + 24x2 + 61x = 0

Reorder the terms:
61x + 24x2 + 3x3 = 0

Solving
61x + 24x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(61 + 24x + 3x2) = 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 '(61 + 24x + 3x2)' equal to zero and attempt to solve:

Simplifying
61 + 24x + 3x2 = 0

Solving
61 + 24x + 3x2 = 0

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

Divide each side by '3'.
20.33333333 + 8x + x2 = 0

Move the constant term to the right:

Add '-20.33333333' to each side of the equation.
20.33333333 + 8x + -20.33333333 + x2 = 0 + -20.33333333

Reorder the terms:
20.33333333 + -20.33333333 + 8x + x2 = 0 + -20.33333333

Combine like terms: 20.33333333 + -20.33333333 = 0.00000000
0.00000000 + 8x + x2 = 0 + -20.33333333
8x + x2 = 0 + -20.33333333

Combine like terms: 0 + -20.33333333 = -20.33333333
8x + x2 = -20.33333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -20.33333333 + 16

Reorder the terms:
16 + 8x + x2 = -20.33333333 + 16

Combine like terms: -20.33333333 + 16 = -4.33333333
16 + 8x + x2 = -4.33333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = -4.33333333

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}