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

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

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

Reorder the terms:
4d(2 + d) + -2d = 3(2 + d)
(2 * 4d + d * 4d) + -2d = 3(2 + d)
(8d + 4d2) + -2d = 3(2 + d)

Reorder the terms:
8d + -2d + 4d2 = 3(2 + d)

Combine like terms: 8d + -2d = 6d
6d + 4d2 = 3(2 + d)
6d + 4d2 = (2 * 3 + d * 3)
6d + 4d2 = (6 + 3d)

Solving
6d + 4d2 = 6 + 3d

Solving for variable 'd'.

Reorder the terms:
-6 + 6d + -3d + 4d2 = 6 + 3d + -6 + -3d

Combine like terms: 6d + -3d = 3d
-6 + 3d + 4d2 = 6 + 3d + -6 + -3d

Reorder the terms:
-6 + 3d + 4d2 = 6 + -6 + 3d + -3d

Combine like terms: 6 + -6 = 0
-6 + 3d + 4d2 = 0 + 3d + -3d
-6 + 3d + 4d2 = 3d + -3d

Combine like terms: 3d + -3d = 0
-6 + 3d + 4d2 = 0

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

Divide each side by '4'.
-1.5 + 0.75d + d2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.75d + 1.5 + d2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.75d + d2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.75d + d2 = 0 + 1.5
0.75d + d2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.75d + d2 = 1.5

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 = 1.5 + 0.140625

Reorder the terms:
0.140625 + 0.75d + d2 = 1.5 + 0.140625

Combine like terms: 1.5 + 0.140625 = 1.640625
0.140625 + 0.75d + d2 = 1.640625

Factor a perfect square on the left side:
(d + 0.375)(d + 0.375) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(d + 0.375) equal to 1.280868846 and -1.280868846.

Subproblem 1
d + 0.375 = 1.280868846

Simplifying
d + 0.375 = 1.280868846

Reorder the terms:
0.375 + d = 1.280868846

Solving
0.375 + d = 1.280868846

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 = 1.280868846 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + d = 1.280868846 + -0.375
d = 1.280868846 + -0.375

Combine like terms: 1.280868846 + -0.375 = 0.905868846
d = 0.905868846

Simplifying
d = 0.905868846

Subproblem 2
d + 0.375 = -1.280868846

Simplifying
d + 0.375 = -1.280868846

Reorder the terms:
0.375 + d = -1.280868846

Solving
0.375 + d = -1.280868846

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 = -1.280868846 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + d = -1.280868846 + -0.375
d = -1.280868846 + -0.375

Combine like terms: -1.280868846 + -0.375 = -1.655868846
d = -1.655868846

Simplifying
d = -1.655868846

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.905868846, -1.655868846}