(2d+6)(3d-15)=0

Solution for (2d+6)(3d-15)=0 equation:

Simplifying
(2d + 6)(3d + -15) = 0

Reorder the terms:
(6 + 2d)(3d + -15) = 0

Reorder the terms:
(6 + 2d)(-15 + 3d) = 0

Multiply (6 + 2d) * (-15 + 3d)
(6(-15 + 3d) + 2d * (-15 + 3d)) = 0
((-15 * 6 + 3d * 6) + 2d * (-15 + 3d)) = 0
((-90 + 18d) + 2d * (-15 + 3d)) = 0
(-90 + 18d + (-15 * 2d + 3d * 2d)) = 0
(-90 + 18d + (-30d + 6d2)) = 0

Combine like terms: 18d + -30d = -12d
(-90 + -12d + 6d2) = 0

Solving
-90 + -12d + 6d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + -2d + d2) = 0

Factor a trinomial.
6((-3 + -1d)(5 + -1d)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -1d)' equal to zero and attempt to solve:

Simplifying
-3 + -1d = 0

Solving
-3 + -1d = 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 + -1d = 0 + 3

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

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

Divide each side by '-1'.
d = -3

Simplifying
d = -3
Subproblem 2
Set the factor '(5 + -1d)' equal to zero and attempt to solve:

Simplifying
5 + -1d = 0

Solving
5 + -1d = 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 + -1d = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1d = 0 + -5
-1d = 0 + -5

Combine like terms: 0 + -5 = -5
-1d = -5

Divide each side by '-1'.
d = 5

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