(2d+3)(3d+1)=0

Solution for (2d+3)(3d+1)=0 equation:

Simplifying
(2d + 3)(3d + 1) = 0

Reorder the terms:
(3 + 2d)(3d + 1) = 0

Reorder the terms:
(3 + 2d)(1 + 3d) = 0

Multiply (3 + 2d) * (1 + 3d)
(3(1 + 3d) + 2d * (1 + 3d)) = 0
((1 * 3 + 3d * 3) + 2d * (1 + 3d)) = 0
((3 + 9d) + 2d * (1 + 3d)) = 0
(3 + 9d + (1 * 2d + 3d * 2d)) = 0
(3 + 9d + (2d + 6d2)) = 0

Combine like terms: 9d + 2d = 11d
(3 + 11d + 6d2) = 0

Solving
3 + 11d + 6d2 = 0

Solving for variable 'd'.

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

Subproblem 1
Set the factor '(3 + 2d)' equal to zero and attempt to solve:

Simplifying
3 + 2d = 0

Solving
3 + 2d = 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 + 2d = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2d = 0 + -3
2d = 0 + -3

Combine like terms: 0 + -3 = -3
2d = -3

Divide each side by '2'.
d = -1.5

Simplifying
d = -1.5
Subproblem 2
Set the factor '(1 + 3d)' equal to zero and attempt to solve:

Simplifying
1 + 3d = 0

Solving
1 + 3d = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3d = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3d = 0 + -1
3d = 0 + -1

Combine like terms: 0 + -1 = -1
3d = -1

Divide each side by '3'.
d = -0.3333333333

Simplifying
d = -0.3333333333
Solution
d = {-1.5, -0.3333333333}