(2d)(2d)-4d-13=3

Solution for (2d)(2d)-4d-13=3 equation:

Simplifying
(2d)(2d) + -4d + -13 = 3

Remove parenthesis around (2d)
2d(2d) + -4d + -13 = 3

Remove parenthesis around (2d)
2d * 2d + -4d + -13 = 3

Reorder the terms for easier multiplication:
2 * 2d * d + -4d + -13 = 3

Multiply 2 * 2
4d * d + -4d + -13 = 3

Multiply d * d
4d2 + -4d + -13 = 3

Reorder the terms:
-13 + -4d + 4d2 = 3

Solving
-13 + -4d + 4d2 = 3

Solving for variable 'd'.

Reorder the terms:
-13 + -3 + -4d + 4d2 = 3 + -3

Combine like terms: -13 + -3 = -16
-16 + -4d + 4d2 = 3 + -3

Combine like terms: 3 + -3 = 0
-16 + -4d + 4d2 = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -1d + d2)' equal to zero and attempt to solve:

Simplifying
-4 + -1d + d2 = 0

Solving
-4 + -1d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1d + 4 + d2 = 0 + 4

Reorder the terms:
-4 + 4 + -1d + d2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1d + d2 = 0 + 4
-1d + d2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1d + d2 = 4

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 = 4 + 0.25

Reorder the terms:
0.25 + -1d + d2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + -1d + d2 = 4.25

Factor a perfect square on the left side:
(d + -0.5)(d + -0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(d + -0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
d + -0.5 = 2.061552813

Simplifying
d + -0.5 = 2.061552813

Reorder the terms:
-0.5 + d = 2.061552813

Solving
-0.5 + d = 2.061552813

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 = 2.061552813 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + d = 2.061552813 + 0.5
d = 2.061552813 + 0.5

Combine like terms: 2.061552813 + 0.5 = 2.561552813
d = 2.561552813

Simplifying
d = 2.561552813

Subproblem 2
d + -0.5 = -2.061552813

Simplifying
d + -0.5 = -2.061552813

Reorder the terms:
-0.5 + d = -2.061552813

Solving
-0.5 + d = -2.061552813

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 = -2.061552813 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + d = -2.061552813 + 0.5
d = -2.061552813 + 0.5

Combine like terms: -2.061552813 + 0.5 = -1.561552813
d = -1.561552813

Simplifying
d = -1.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.561552813, -1.561552813}
Solution
d = {2.561552813, -1.561552813}