24x^3+12x^2+15x=0

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Solution for 24x^3+12x^2+15x=0 equation: 


Simplifying
24x3 + 12x2 + 15x = 0

Reorder the terms:
15x + 12x2 + 24x3 = 0

Solving
15x + 12x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(5 + 4x + 8x2) = 0

Ignore the factor 3.

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 '(5 + 4x + 8x2)' equal to zero and attempt to solve:

Simplifying
5 + 4x + 8x2 = 0

Solving
5 + 4x + 8x2 = 0

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

Divide each side by '8'.
0.625 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + 0.5x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + 0.5x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + 0.5x + x2 = 0 + -0.625
0.5x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
0.5x + x2 = -0.625

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.625 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.625 + 0.0625

Combine like terms: -0.625 + 0.0625 = -0.5625
0.0625 + 0.5x + x2 = -0.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -0.5625

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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