(3d+6)(5d-15)=0

Solution for (3d+6)(5d-15)=0 equation:

Simplifying
(3d + 6)(5d + -15) = 0

Reorder the terms:
(6 + 3d)(5d + -15) = 0

Reorder the terms:
(6 + 3d)(-15 + 5d) = 0

Multiply (6 + 3d) * (-15 + 5d)
(6(-15 + 5d) + 3d * (-15 + 5d)) = 0
((-15 * 6 + 5d * 6) + 3d * (-15 + 5d)) = 0
((-90 + 30d) + 3d * (-15 + 5d)) = 0
(-90 + 30d + (-15 * 3d + 5d * 3d)) = 0
(-90 + 30d + (-45d + 15d2)) = 0

Combine like terms: 30d + -45d = -15d
(-90 + -15d + 15d2) = 0

Solving
-90 + -15d + 15d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-6 + -1d + d2) = 0

Factor a trinomial.
15((-2 + -1d)(3 + -1d)) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-2 + -1d)' equal to zero and attempt to solve:

Simplifying
-2 + -1d = 0

Solving
-2 + -1d = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1d = 0 + 2

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

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

Divide each side by '-1'.
d = -2

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