(d^3+d^2-4d)y=0

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Solution for (d^3+d^2-4d)y=0 equation: 


Simplifying
(d3 + d2 + -4d) * y = 0

Reorder the terms:
(-4d + d2 + d3) * y = 0

Reorder the terms for easier multiplication:
y(-4d + d2 + d3) = 0
(-4d * y + d2 * y + d3 * y) = 0
(-4dy + d2y + d3y) = 0

Solving
-4dy + d2y + d3y = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'dy'.
dy(-4 + d + d2) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-4 + d + d2)' equal to zero and attempt to solve:

Simplifying
-4 + d + d2 = 0

Solving
-4 + d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + d + 4 + d2 = 0 + 4

Reorder the terms:
-4 + 4 + d + d2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + d + d2 = 0 + 4
d + d2 = 0 + 4

Combine like terms: 0 + 4 = 4
d + d2 = 4

The d term is d.  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.
d + 0.25 + d2 = 4 + 0.25

Reorder the terms:
0.25 + d + d2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + d + d2 = 4.25

Factor a perfect square on the left side:
(d + 0.5)(d + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(d + 0.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
d + 0.5 = 2.061552813

Simplifying
d + 0.5 = 2.061552813

Reorder the terms:
0.5 + d = 2.061552813

Solving
0.5 + d = 2.061552813

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = 2.061552813 + -0.5
d = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
d = 1.561552813

Simplifying
d = 1.561552813


Subproblem 2
d + 0.5 = -2.061552813

Simplifying
d + 0.5 = -2.061552813

Reorder the terms:
0.5 + d = -2.061552813

Solving
0.5 + d = -2.061552813

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = -2.061552813 + -0.5
d = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
d = -2.561552813

Simplifying
d = -2.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {1.561552813, -2.561552813}
Solution
d = {1.561552813, -2.561552813}

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