4(2.2d-1).8d=23

Solution for 4(2.2d-1).8d=23 equation:

Simplifying
4(2.2d + -1) * 0.8d = 23

Reorder the terms:
4(-1 + 2.2d) * 0.8d = 23

Reorder the terms for easier multiplication:
4 * 0.8d(-1 + 2.2d) = 23

Multiply 4 * 0.8
3.2d(-1 + 2.2d) = 23
(-1 * 3.2d + 2.2d * 3.2d) = 23
(-3.2d + 7.04d2) = 23

Solving
-3.2d + 7.04d2 = 23

Solving for variable 'd'.

Reorder the terms:
-23 + -3.2d + 7.04d2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -3.2d + 7.04d2 = 0

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

Divide each side by '7.04'.
-3.267045455 + -0.4545454545d + d2 = 0

Move the constant term to the right:

Add '3.267045455' to each side of the equation.
-3.267045455 + -0.4545454545d + 3.267045455 + d2 = 0 + 3.267045455

Reorder the terms:
-3.267045455 + 3.267045455 + -0.4545454545d + d2 = 0 + 3.267045455

Combine like terms: -3.267045455 + 3.267045455 = 0.000000000
0.000000000 + -0.4545454545d + d2 = 0 + 3.267045455
-0.4545454545d + d2 = 0 + 3.267045455

Combine like terms: 0 + 3.267045455 = 3.267045455
-0.4545454545d + d2 = 3.267045455

The d term is -0.4545454545d.  Take half its coefficient (-0.2272727273).
Square it (0.05165289257) and add it to both sides.

Add '0.05165289257' to each side of the equation.
-0.4545454545d + 0.05165289257 + d2 = 3.267045455 + 0.05165289257

Reorder the terms:
0.05165289257 + -0.4545454545d + d2 = 3.267045455 + 0.05165289257

Combine like terms: 3.267045455 + 0.05165289257 = 3.31869834757
0.05165289257 + -0.4545454545d + d2 = 3.31869834757

Factor a perfect square on the left side:
(d + -0.2272727273)(d + -0.2272727273) = 3.31869834757

Calculate the square root of the right side: 1.821729494

Break this problem into two subproblems by setting 
(d + -0.2272727273) equal to 1.821729494 and -1.821729494.

Subproblem 1
d + -0.2272727273 = 1.821729494

Simplifying
d + -0.2272727273 = 1.821729494

Reorder the terms:
-0.2272727273 + d = 1.821729494

Solving
-0.2272727273 + d = 1.821729494

Solving for variable 'd'.

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

Add '0.2272727273' to each side of the equation.
-0.2272727273 + 0.2272727273 + d = 1.821729494 + 0.2272727273

Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000
0.0000000000 + d = 1.821729494 + 0.2272727273
d = 1.821729494 + 0.2272727273

Combine like terms: 1.821729494 + 0.2272727273 = 2.0490022213
d = 2.0490022213

Simplifying
d = 2.0490022213

Subproblem 2
d + -0.2272727273 = -1.821729494

Simplifying
d + -0.2272727273 = -1.821729494

Reorder the terms:
-0.2272727273 + d = -1.821729494

Solving
-0.2272727273 + d = -1.821729494

Solving for variable 'd'.

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

Add '0.2272727273' to each side of the equation.
-0.2272727273 + 0.2272727273 + d = -1.821729494 + 0.2272727273

Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000
0.0000000000 + d = -1.821729494 + 0.2272727273
d = -1.821729494 + 0.2272727273

Combine like terms: -1.821729494 + 0.2272727273 = -1.5944567667
d = -1.5944567667

Simplifying
d = -1.5944567667

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.0490022213, -1.5944567667}