16y^3+8y^2+24y=0

Solution for 16y^3+8y^2+24y=0 equation:

Simplifying
16y3 + 8y2 + 24y = 0

Reorder the terms:
24y + 8y2 + 16y3 = 0

Solving
24y + 8y2 + 16y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '8y'.
8y(3 + y + 2y2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(3 + y + 2y2)' equal to zero and attempt to solve:

Simplifying
3 + y + 2y2 = 0

Solving
3 + y + 2y2 = 0

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

Divide each side by '2'.
1.5 + 0.5y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.5y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.5y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.5y + y2 = 0 + -1.5
0.5y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.5y + y2 = -1.5

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

Add '0.25' to each side of the equation.
0.5y + 0.25 + y2 = -1.5 + 0.25

Reorder the terms:
0.25 + 0.5y + y2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + 0.5y + y2 = -1.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -1.25

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
y = {0}