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

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

Simplifying
(4d + 2)(d + 3) = 0

Reorder the terms:
(2 + 4d)(d + 3) = 0

Reorder the terms:
(2 + 4d)(3 + d) = 0

Multiply (2 + 4d) * (3 + d)
(2(3 + d) + 4d * (3 + d)) = 0
((3 * 2 + d * 2) + 4d * (3 + d)) = 0
((6 + 2d) + 4d * (3 + d)) = 0
(6 + 2d + (3 * 4d + d * 4d)) = 0
(6 + 2d + (12d + 4d2)) = 0

Combine like terms: 2d + 12d = 14d
(6 + 14d + 4d2) = 0

Solving
6 + 14d + 4d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 7d + 2d2) = 0

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

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

Simplifying
3 + d = 0

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

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

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

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

Simplifying
1 + 2d = 0

Solving
1 + 2d = 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 + 2d = 0 + -1

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

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

Divide each side by '2'.
d = -0.5

Simplifying
d = -0.5
Solution
d = {-3, -0.5}