-4d^2-76d-20=0

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Solution for -4d^2-76d-20=0 equation: 


Simplifying
-4d2 + -76d + -20 = 0

Reorder the terms:
-20 + -76d + -4d2 = 0

Solving
-20 + -76d + -4d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(5 + 19d + d2) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(5 + 19d + d2)' equal to zero and attempt to solve:

Simplifying
5 + 19d + d2 = 0

Solving
5 + 19d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 19d + -5 + d2 = 0 + -5

Reorder the terms:
5 + -5 + 19d + d2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 19d + d2 = 0 + -5
19d + d2 = 0 + -5

Combine like terms: 0 + -5 = -5
19d + d2 = -5

The d term is 19d.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19d + 90.25 + d2 = -5 + 90.25

Reorder the terms:
90.25 + 19d + d2 = -5 + 90.25

Combine like terms: -5 + 90.25 = 85.25
90.25 + 19d + d2 = 85.25

Factor a perfect square on the left side:
(d + 9.5)(d + 9.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(d + 9.5) equal to 9.233092656 and -9.233092656.


Subproblem 1
d + 9.5 = 9.233092656

Simplifying
d + 9.5 = 9.233092656

Reorder the terms:
9.5 + d = 9.233092656

Solving
9.5 + d = 9.233092656

Solving for variable 'd'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + d = 9.233092656 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + d = 9.233092656 + -9.5
d = 9.233092656 + -9.5

Combine like terms: 9.233092656 + -9.5 = -0.266907344
d = -0.266907344

Simplifying
d = -0.266907344


Subproblem 2
d + 9.5 = -9.233092656

Simplifying
d + 9.5 = -9.233092656

Reorder the terms:
9.5 + d = -9.233092656

Solving
9.5 + d = -9.233092656

Solving for variable 'd'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + d = -9.233092656 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + d = -9.233092656 + -9.5
d = -9.233092656 + -9.5

Combine like terms: -9.233092656 + -9.5 = -18.733092656
d = -18.733092656

Simplifying
d = -18.733092656


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.266907344, -18.733092656}
Solution
d = {-0.266907344, -18.733092656}

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