(d+12)(4d+6)=0

Solution for (d+12)(4d+6)=0 equation:

Simplifying
(d + 12)(4d + 6) = 0

Reorder the terms:
(12 + d)(4d + 6) = 0

Reorder the terms:
(12 + d)(6 + 4d) = 0

Multiply (12 + d) * (6 + 4d)
(12(6 + 4d) + d(6 + 4d)) = 0
((6 * 12 + 4d * 12) + d(6 + 4d)) = 0
((72 + 48d) + d(6 + 4d)) = 0
(72 + 48d + (6 * d + 4d * d)) = 0
(72 + 48d + (6d + 4d2)) = 0

Combine like terms: 48d + 6d = 54d
(72 + 54d + 4d2) = 0

Solving
72 + 54d + 4d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 27d + 2d2) = 0

Factor a trinomial.
2((12 + d)(3 + 2d)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + d)' equal to zero and attempt to solve:

Simplifying
12 + d = 0

Solving
12 + d = 0

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

Add '-12' to each side of the equation.
12 + -12 + d = 0 + -12

Combine like terms: 12 + -12 = 0
0 + d = 0 + -12
d = 0 + -12

Combine like terms: 0 + -12 = -12
d = -12

Simplifying
d = -12
Subproblem 2
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
Solution
d = {-12, -1.5}