40=1.6d(d-2)

Solution for 40=1.6d(d-2) equation:

Simplifying
40 = 1.6d(d + -2)

Reorder the terms:
40 = 1.6d(-2 + d)
40 = (-2 * 1.6d + d * 1.6d)
40 = (-3.2d + 1.6d2)

Solving
40 = -3.2d + 1.6d2

Solving for variable 'd'.

Reorder the terms:
40 + 3.2d + -1.6d2 = -3.2d + 3.2d + 1.6d2 + -1.6d2

Combine like terms: -3.2d + 3.2d = 0.0
40 + 3.2d + -1.6d2 = 0.0 + 1.6d2 + -1.6d2
40 + 3.2d + -1.6d2 = 1.6d2 + -1.6d2

Combine like terms: 1.6d2 + -1.6d2 = 0.0
40 + 3.2d + -1.6d2 = 0.0

Begin completing the square.  Divide all terms by
-1.6 the coefficient of the squared term: 

Divide each side by '-1.6'.
-25 + -2d + d2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -2d + 25 + d2 = 0 + 25

Reorder the terms:
-25 + 25 + -2d + d2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2d + d2 = 0 + 25
-2d + d2 = 0 + 25

Combine like terms: 0 + 25 = 25
-2d + d2 = 25

The d term is -2d.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2d + 1 + d2 = 25 + 1

Reorder the terms:
1 + -2d + d2 = 25 + 1

Combine like terms: 25 + 1 = 26
1 + -2d + d2 = 26

Factor a perfect square on the left side:
(d + -1)(d + -1) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(d + -1) equal to 5.099019514 and -5.099019514.

Subproblem 1
d + -1 = 5.099019514

Simplifying
d + -1 = 5.099019514

Reorder the terms:
-1 + d = 5.099019514

Solving
-1 + d = 5.099019514

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = 5.099019514 + 1

Combine like terms: -1 + 1 = 0
0 + d = 5.099019514 + 1
d = 5.099019514 + 1

Combine like terms: 5.099019514 + 1 = 6.099019514
d = 6.099019514

Simplifying
d = 6.099019514

Subproblem 2
d + -1 = -5.099019514

Simplifying
d + -1 = -5.099019514

Reorder the terms:
-1 + d = -5.099019514

Solving
-1 + d = -5.099019514

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = -5.099019514 + 1

Combine like terms: -1 + 1 = 0
0 + d = -5.099019514 + 1
d = -5.099019514 + 1

Combine like terms: -5.099019514 + 1 = -4.099019514
d = -4.099019514

Simplifying
d = -4.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {6.099019514, -4.099019514}