.25d(d-12)=4

Solution for .25d(d-12)=4 equation:

Simplifying
0.25d(d + -12) = 4

Reorder the terms:
0.25d(-12 + d) = 4
(-12 * 0.25d + d * 0.25d) = 4
(-3d + 0.25d2) = 4

Solving
-3d + 0.25d2 = 4

Solving for variable 'd'.

Reorder the terms:
-4 + -3d + 0.25d2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -3d + 0.25d2 = 0

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

Divide each side by '0.25'.
-16 + -12d + d2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -12d + 16 + d2 = 0 + 16

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

Combine like terms: -16 + 16 = 0
0 + -12d + d2 = 0 + 16
-12d + d2 = 0 + 16

Combine like terms: 0 + 16 = 16
-12d + d2 = 16

The d term is -12d.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12d + 36 + d2 = 16 + 36

Reorder the terms:
36 + -12d + d2 = 16 + 36

Combine like terms: 16 + 36 = 52
36 + -12d + d2 = 52

Factor a perfect square on the left side:
(d + -6)(d + -6) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(d + -6) equal to 7.211102551 and -7.211102551.

Subproblem 1
d + -6 = 7.211102551

Simplifying
d + -6 = 7.211102551

Reorder the terms:
-6 + d = 7.211102551

Solving
-6 + d = 7.211102551

Solving for variable 'd'.

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

Add '6' to each side of the equation.
-6 + 6 + d = 7.211102551 + 6

Combine like terms: -6 + 6 = 0
0 + d = 7.211102551 + 6
d = 7.211102551 + 6

Combine like terms: 7.211102551 + 6 = 13.211102551
d = 13.211102551

Simplifying
d = 13.211102551

Subproblem 2
d + -6 = -7.211102551

Simplifying
d + -6 = -7.211102551

Reorder the terms:
-6 + d = -7.211102551

Solving
-6 + d = -7.211102551

Solving for variable 'd'.

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

Add '6' to each side of the equation.
-6 + 6 + d = -7.211102551 + 6

Combine like terms: -6 + 6 = 0
0 + d = -7.211102551 + 6
d = -7.211102551 + 6

Combine like terms: -7.211102551 + 6 = -1.211102551
d = -1.211102551

Simplifying
d = -1.211102551

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {13.211102551, -1.211102551}