(4d^2-36)-4d-12=48

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Solution for (4d^2-36)-4d-12=48 equation: 


Simplifying
(4d2 + -36) + -4d + -12 = 48

Reorder the terms:
(-36 + 4d2) + -4d + -12 = 48

Remove parenthesis around (-36 + 4d2)
-36 + 4d2 + -4d + -12 = 48

Reorder the terms:
-36 + -12 + -4d + 4d2 = 48

Combine like terms: -36 + -12 = -48
-48 + -4d + 4d2 = 48

Solving
-48 + -4d + 4d2 = 48

Solving for variable 'd'.

Reorder the terms:
-48 + -48 + -4d + 4d2 = 48 + -48

Combine like terms: -48 + -48 = -96
-96 + -4d + 4d2 = 48 + -48

Combine like terms: 48 + -48 = 0
-96 + -4d + 4d2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + -1d + d2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-24 + -1d + d2)' equal to zero and attempt to solve:

Simplifying
-24 + -1d + d2 = 0

Solving
-24 + -1d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -1d + 24 + d2 = 0 + 24

Reorder the terms:
-24 + 24 + -1d + d2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1d + d2 = 0 + 24
-1d + d2 = 0 + 24

Combine like terms: 0 + 24 = 24
-1d + d2 = 24

The d term is -1d.  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.
-1d + 0.25 + d2 = 24 + 0.25

Reorder the terms:
0.25 + -1d + d2 = 24 + 0.25

Combine like terms: 24 + 0.25 = 24.25
0.25 + -1d + d2 = 24.25

Factor a perfect square on the left side:
(d + -0.5)(d + -0.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(d + -0.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
d + -0.5 = 4.924428901

Simplifying
d + -0.5 = 4.924428901

Reorder the terms:
-0.5 + d = 4.924428901

Solving
-0.5 + d = 4.924428901

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 = 4.924428901 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + d = 4.924428901 + 0.5
d = 4.924428901 + 0.5

Combine like terms: 4.924428901 + 0.5 = 5.424428901
d = 5.424428901

Simplifying
d = 5.424428901


Subproblem 2
d + -0.5 = -4.924428901

Simplifying
d + -0.5 = -4.924428901

Reorder the terms:
-0.5 + d = -4.924428901

Solving
-0.5 + d = -4.924428901

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 = -4.924428901 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + d = -4.924428901 + 0.5
d = -4.924428901 + 0.5

Combine like terms: -4.924428901 + 0.5 = -4.424428901
d = -4.424428901

Simplifying
d = -4.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {5.424428901, -4.424428901}
Solution
d = {5.424428901, -4.424428901}

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