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

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

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

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

Reorder the terms for easier multiplication:
4 * 2d(2 + d) = 3(2 + d)

Multiply 4 * 2
8d(2 + d) = 3(2 + d)
(2 * 8d + d * 8d) = 3(2 + d)
(16d + 8d2) = 3(2 + d)
16d + 8d2 = (2 * 3 + d * 3)
16d + 8d2 = (6 + 3d)

Solving
16d + 8d2 = 6 + 3d

Solving for variable 'd'.

Reorder the terms:
-6 + 16d + -3d + 8d2 = 6 + 3d + -6 + -3d

Combine like terms: 16d + -3d = 13d
-6 + 13d + 8d2 = 6 + 3d + -6 + -3d

Reorder the terms:
-6 + 13d + 8d2 = 6 + -6 + 3d + -3d

Combine like terms: 6 + -6 = 0
-6 + 13d + 8d2 = 0 + 3d + -3d
-6 + 13d + 8d2 = 3d + -3d

Combine like terms: 3d + -3d = 0
-6 + 13d + 8d2 = 0

Factor a trinomial.
(-2 + -1d)(3 + -8d) = 0

Subproblem 1
Set the factor '(-2 + -1d)' equal to zero and attempt to solve:

Simplifying
-2 + -1d = 0

Solving
-2 + -1d = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1d = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1d = 0 + 2
-1d = 0 + 2

Combine like terms: 0 + 2 = 2
-1d = 2

Divide each side by '-1'.
d = -2

Simplifying
d = -2
Subproblem 2
Set the factor '(3 + -8d)' equal to zero and attempt to solve:

Simplifying
3 + -8d = 0

Solving
3 + -8d = 0

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

Add '-3' to each side of the equation.
3 + -3 + -8d = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8d = 0 + -3
-8d = 0 + -3

Combine like terms: 0 + -3 = -3
-8d = -3

Divide each side by '-8'.
d = 0.375

Simplifying
d = 0.375
Solution
d = {-2, 0.375}