20d^3+8d^2+24d=

Solution for 20d^3+8d^2+24d= equation:

Simplifying
20d3 + 8d2 + 24d = 0

Reorder the terms:
24d + 8d2 + 20d3 = 0

Solving
24d + 8d2 + 20d3 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '4d'.
4d(6 + 2d + 5d2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0
Subproblem 2
Set the factor '(6 + 2d + 5d2)' equal to zero and attempt to solve:

Simplifying
6 + 2d + 5d2 = 0

Solving
6 + 2d + 5d2 = 0

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

Divide each side by '5'.
1.2 + 0.4d + d2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 0.4d + -1.2 + d2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 0.4d + d2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 0.4d + d2 = 0 + -1.2
0.4d + d2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
0.4d + d2 = -1.2

The d term is 0.4d.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4d + 0.04 + d2 = -1.2 + 0.04

Reorder the terms:
0.04 + 0.4d + d2 = -1.2 + 0.04

Combine like terms: -1.2 + 0.04 = -1.16
0.04 + 0.4d + d2 = -1.16

Factor a perfect square on the left side:
(d + 0.2)(d + 0.2) = -1.16

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
d = {0}