(2d*2d)+12d-30=0

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Solution for (2d*2d)+12d-30=0 equation: 


Simplifying
(2d * 2d) + 12d + -30 = 0

Reorder the terms for easier multiplication:
(2 * 2d * d) + 12d + -30 = 0

Multiply 2 * 2
(4d * d) + 12d + -30 = 0

Multiply d * d
(4d2) + 12d + -30 = 0

Reorder the terms:
-30 + 12d + (4d2) = 0

Solving
-30 + 12d + (4d2) = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 6d + (2d2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 6d + (2d2))' equal to zero and attempt to solve:

Simplifying
-15 + 6d + (2d2) = 0

Solving
-15 + 6d + (2d2) = 0

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

Divide each side by '2'.
-7.5 + 3d + d2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 3d + 7.5 + d2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 3d + d2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 3d + d2 = 0 + 7.5
3d + d2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
3d + d2 = 7.5

The d term is 3d.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3d + 2.25 + d2 = 7.5 + 2.25

Reorder the terms:
2.25 + 3d + d2 = 7.5 + 2.25

Combine like terms: 7.5 + 2.25 = 9.75
2.25 + 3d + d2 = 9.75

Factor a perfect square on the left side:
((d) + 1.5)((d) + 1.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
((d) + 1.5) equal to 3.122498999 and -3.122498999.


Subproblem 1
(d) + 1.5 = 3.122498999

Simplifying
(d) + 1.5 = 3.122498999
d + 1.5 = 3.122498999

Reorder the terms:
1.5 + d = 3.122498999

Solving
1.5 + d = 3.122498999

Solving for variable 'd'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + d = 3.122498999 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + d = 3.122498999 + -1.5
d = 3.122498999 + -1.5

Combine like terms: 3.122498999 + -1.5 = 1.622498999
d = 1.622498999

Simplifying
d = 1.622498999


Subproblem 2
(d) + 1.5 = -3.122498999

Simplifying
(d) + 1.5 = -3.122498999
d + 1.5 = -3.122498999

Reorder the terms:
1.5 + d = -3.122498999

Solving
1.5 + d = -3.122498999

Solving for variable 'd'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + d = -3.122498999 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + d = -3.122498999 + -1.5
d = -3.122498999 + -1.5

Combine like terms: -3.122498999 + -1.5 = -4.622498999
d = -4.622498999

Simplifying
d = -4.622498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {1.622498999, -4.622498999}
Solution
d = {1.622498999, -4.622498999}

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