3(d+3)(d+5)=0

Solution for 3(d+3)(d+5)=0 equation:

Simplifying
3(d + 3)(d + 5) = 0

Reorder the terms:
3(3 + d)(d + 5) = 0

Reorder the terms:
3(3 + d)(5 + d) = 0

Multiply (3 + d) * (5 + d)
3(3(5 + d) + d(5 + d)) = 0
3((5 * 3 + d * 3) + d(5 + d)) = 0
3((15 + 3d) + d(5 + d)) = 0
3(15 + 3d + (5 * d + d * d)) = 0
3(15 + 3d + (5d + d2)) = 0

Combine like terms: 3d + 5d = 8d
3(15 + 8d + d2) = 0
(15 * 3 + 8d * 3 + d2 * 3) = 0
(45 + 24d + 3d2) = 0

Solving
45 + 24d + 3d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 8d + d2) = 0

Factor a trinomial.
3((5 + d)(3 + d)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + d)' equal to zero and attempt to solve:

Simplifying
5 + d = 0

Solving
5 + d = 0

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

Add '-5' to each side of the equation.
5 + -5 + d = 0 + -5

Combine like terms: 5 + -5 = 0
0 + d = 0 + -5
d = 0 + -5

Combine like terms: 0 + -5 = -5
d = -5

Simplifying
d = -5
Subproblem 2
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
Solution
d = {-5, -3}