3d^2-51d+162=0

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Solution for 3d^2-51d+162=0 equation: 


Simplifying
3d2 + -51d + 162 = 0

Reorder the terms:
162 + -51d + 3d2 = 0

Solving
162 + -51d + 3d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3'.
3(54 + -17d + d2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(54 + -17d + d2)' equal to zero and attempt to solve:

Simplifying
54 + -17d + d2 = 0

Solving
54 + -17d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -17d + -54 + d2 = 0 + -54

Reorder the terms:
54 + -54 + -17d + d2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -17d + d2 = 0 + -54
-17d + d2 = 0 + -54

Combine like terms: 0 + -54 = -54
-17d + d2 = -54

The d term is -17d.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17d + 72.25 + d2 = -54 + 72.25

Reorder the terms:
72.25 + -17d + d2 = -54 + 72.25

Combine like terms: -54 + 72.25 = 18.25
72.25 + -17d + d2 = 18.25

Factor a perfect square on the left side:
(d + -8.5)(d + -8.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(d + -8.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
d + -8.5 = 4.272001873

Simplifying
d + -8.5 = 4.272001873

Reorder the terms:
-8.5 + d = 4.272001873

Solving
-8.5 + d = 4.272001873

Solving for variable 'd'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + d = 4.272001873 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + d = 4.272001873 + 8.5
d = 4.272001873 + 8.5

Combine like terms: 4.272001873 + 8.5 = 12.772001873
d = 12.772001873

Simplifying
d = 12.772001873


Subproblem 2
d + -8.5 = -4.272001873

Simplifying
d + -8.5 = -4.272001873

Reorder the terms:
-8.5 + d = -4.272001873

Solving
-8.5 + d = -4.272001873

Solving for variable 'd'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + d = -4.272001873 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + d = -4.272001873 + 8.5
d = -4.272001873 + 8.5

Combine like terms: -4.272001873 + 8.5 = 4.227998127
d = 4.227998127

Simplifying
d = 4.227998127


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {12.772001873, 4.227998127}
Solution
d = {12.772001873, 4.227998127}

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