18d^4+36d^3+9d^2=

Solution for 18d^4+36d^3+9d^2= equation:

Simplifying
18d4 + 36d3 + 9d2 = 0

Reorder the terms:
9d2 + 36d3 + 18d4 = 0

Solving
9d2 + 36d3 + 18d4 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '9d2'.
9d2(1 + 4d + 2d2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor 'd2' equal to zero and attempt to solve:

Simplifying
d2 = 0

Solving
d2 = 0

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

Simplifying
d2 = 0

Take the square root of each side:
d = {0}
Subproblem 2
Set the factor '(1 + 4d + 2d2)' equal to zero and attempt to solve:

Simplifying
1 + 4d + 2d2 = 0

Solving
1 + 4d + 2d2 = 0

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

Divide each side by '2'.
0.5 + 2d + d2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2d + -0.5 + d2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2d + d2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2d + d2 = 0 + -0.5
2d + d2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2d + d2 = -0.5

The d term is 2d.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2d + 1 + d2 = -0.5 + 1

Reorder the terms:
1 + 2d + d2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + 2d + d2 = 0.5

Factor a perfect square on the left side:
(d + 1)(d + 1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(d + 1) equal to 0.707106781 and -0.707106781.

Subproblem 1
d + 1 = 0.707106781

Simplifying
d + 1 = 0.707106781

Reorder the terms:
1 + d = 0.707106781

Solving
1 + d = 0.707106781

Solving for variable 'd'.

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

Add '-1' to each side of the equation.
1 + -1 + d = 0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + d = 0.707106781 + -1
d = 0.707106781 + -1

Combine like terms: 0.707106781 + -1 = -0.292893219
d = -0.292893219

Simplifying
d = -0.292893219

Subproblem 2
d + 1 = -0.707106781

Simplifying
d + 1 = -0.707106781

Reorder the terms:
1 + d = -0.707106781

Solving
1 + d = -0.707106781

Solving for variable 'd'.

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

Add '-1' to each side of the equation.
1 + -1 + d = -0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + d = -0.707106781 + -1
d = -0.707106781 + -1

Combine like terms: -0.707106781 + -1 = -1.707106781
d = -1.707106781

Simplifying
d = -1.707106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.292893219, -1.707106781}
Solution
d = {0, -0.292893219, -1.707106781}