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

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Solution for (4d*4d)+12d-30=0 equation: 


Simplifying
(4d * 4d) + 12d + -30 = 0

Reorder the terms for easier multiplication:
(4 * 4d * d) + 12d + -30 = 0

Multiply 4 * 4
(16d * d) + 12d + -30 = 0

Multiply d * d
(16d2) + 12d + -30 = 0

Reorder the terms:
-30 + 12d + (16d2) = 0

Solving
-30 + 12d + (16d2) = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 6d + (8d2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 6d + (8d2))' equal to zero and attempt to solve:

Simplifying
-15 + 6d + (8d2) = 0

Solving
-15 + 6d + (8d2) = 0

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

Divide each side by '8'.
-1.875 + 0.75d + d2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 0.75d + 1.875 + d2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 0.75d + d2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 0.75d + d2 = 0 + 1.875
0.75d + d2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
0.75d + d2 = 1.875

The d term is 0.75d.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75d + 0.140625 + d2 = 1.875 + 0.140625

Reorder the terms:
0.140625 + 0.75d + d2 = 1.875 + 0.140625

Combine like terms: 1.875 + 0.140625 = 2.015625
0.140625 + 0.75d + d2 = 2.015625

Factor a perfect square on the left side:
((d) + 0.375)((d) + 0.375) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
((d) + 0.375) equal to 1.419727086 and -1.419727086.


Subproblem 1
(d) + 0.375 = 1.419727086

Simplifying
(d) + 0.375 = 1.419727086
d + 0.375 = 1.419727086

Reorder the terms:
0.375 + d = 1.419727086

Solving
0.375 + d = 1.419727086

Solving for variable 'd'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + d = 1.419727086 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + d = 1.419727086 + -0.375
d = 1.419727086 + -0.375

Combine like terms: 1.419727086 + -0.375 = 1.044727086
d = 1.044727086

Simplifying
d = 1.044727086


Subproblem 2
(d) + 0.375 = -1.419727086

Simplifying
(d) + 0.375 = -1.419727086
d + 0.375 = -1.419727086

Reorder the terms:
0.375 + d = -1.419727086

Solving
0.375 + d = -1.419727086

Solving for variable 'd'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + d = -1.419727086 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + d = -1.419727086 + -0.375
d = -1.419727086 + -0.375

Combine like terms: -1.419727086 + -0.375 = -1.794727086
d = -1.794727086

Simplifying
d = -1.794727086


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {1.044727086, -1.794727086}
Solution
d = {1.044727086, -1.794727086}

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