8(2d-3)=3d(4d-7)

Solution for 8(2d-3)=3d(4d-7) equation:

Simplifying
8(2d + -3) = 3d(4d + -7)

Reorder the terms:
8(-3 + 2d) = 3d(4d + -7)
(-3 * 8 + 2d * 8) = 3d(4d + -7)
(-24 + 16d) = 3d(4d + -7)

Reorder the terms:
-24 + 16d = 3d(-7 + 4d)
-24 + 16d = (-7 * 3d + 4d * 3d)
-24 + 16d = (-21d + 12d2)

Solving
-24 + 16d = -21d + 12d2

Solving for variable 'd'.

Combine like terms: 16d + 21d = 37d
-24 + 37d + -12d2 = -21d + 12d2 + 21d + -12d2

Reorder the terms:
-24 + 37d + -12d2 = -21d + 21d + 12d2 + -12d2

Combine like terms: -21d + 21d = 0
-24 + 37d + -12d2 = 0 + 12d2 + -12d2
-24 + 37d + -12d2 = 12d2 + -12d2

Combine like terms: 12d2 + -12d2 = 0
-24 + 37d + -12d2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
2 + -3.083333333d + d2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.083333333d + -2 + d2 = 0 + -2

Reorder the terms:
2 + -2 + -3.083333333d + d2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.083333333d + d2 = 0 + -2
-3.083333333d + d2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.083333333d + d2 = -2

The d term is -3.083333333d.  Take half its coefficient (-1.541666667).
Square it (2.376736112) and add it to both sides.

Add '2.376736112' to each side of the equation.
-3.083333333d + 2.376736112 + d2 = -2 + 2.376736112

Reorder the terms:
2.376736112 + -3.083333333d + d2 = -2 + 2.376736112

Combine like terms: -2 + 2.376736112 = 0.376736112
2.376736112 + -3.083333333d + d2 = 0.376736112

Factor a perfect square on the left side:
(d + -1.541666667)(d + -1.541666667) = 0.376736112

Calculate the square root of the right side: 0.613788328

Break this problem into two subproblems by setting 
(d + -1.541666667) equal to 0.613788328 and -0.613788328.

Subproblem 1
d + -1.541666667 = 0.613788328

Simplifying
d + -1.541666667 = 0.613788328

Reorder the terms:
-1.541666667 + d = 0.613788328

Solving
-1.541666667 + d = 0.613788328

Solving for variable 'd'.

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

Add '1.541666667' to each side of the equation.
-1.541666667 + 1.541666667 + d = 0.613788328 + 1.541666667

Combine like terms: -1.541666667 + 1.541666667 = 0.000000000
0.000000000 + d = 0.613788328 + 1.541666667
d = 0.613788328 + 1.541666667

Combine like terms: 0.613788328 + 1.541666667 = 2.155454995
d = 2.155454995

Simplifying
d = 2.155454995

Subproblem 2
d + -1.541666667 = -0.613788328

Simplifying
d + -1.541666667 = -0.613788328

Reorder the terms:
-1.541666667 + d = -0.613788328

Solving
-1.541666667 + d = -0.613788328

Solving for variable 'd'.

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

Add '1.541666667' to each side of the equation.
-1.541666667 + 1.541666667 + d = -0.613788328 + 1.541666667

Combine like terms: -1.541666667 + 1.541666667 = 0.000000000
0.000000000 + d = -0.613788328 + 1.541666667
d = -0.613788328 + 1.541666667

Combine like terms: -0.613788328 + 1.541666667 = 0.927878339
d = 0.927878339

Simplifying
d = 0.927878339

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.155454995, 0.927878339}