6d^2+21d+15=0

Solution for 6d^2+21d+15=0 equation:

Simplifying
6d2 + 21d + 15 = 0

Reorder the terms:
15 + 21d + 6d2 = 0

Solving
15 + 21d + 6d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 7d + 2d2) = 0

Factor a trinomial.
3((5 + 2d)(1 + d)) = 0

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

Simplifying
5 + 2d = 0

Solving
5 + 2d = 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 + 2d = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2d = 0 + -5
2d = 0 + -5

Combine like terms: 0 + -5 = -5
2d = -5

Divide each side by '2'.
d = -2.5

Simplifying
d = -2.5
Subproblem 2
Set the factor '(1 + d)' equal to zero and attempt to solve:

Simplifying
1 + d = 0

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

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

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

Simplifying
d = -1
Solution
d = {-2.5, -1}