6d^2+21d+18=0

Solution for 6d^2+21d+18=0 equation:

Simplifying
6d2 + 21d + 18 = 0

Reorder the terms:
18 + 21d + 6d2 = 0

Solving
18 + 21d + 6d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 7d + 2d2) = 0

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

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

Simplifying
2 + d = 0

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

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

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

Simplifying
d = -2
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 = {-2, -1.5}