(d^2+5d+6)y=0

Solution for (d^2+5d+6)y=0 equation:

Simplifying
(d2 + 5d + 6) * y = 0

Reorder the terms:
(6 + 5d + d2) * y = 0

Reorder the terms for easier multiplication:
y(6 + 5d + d2) = 0
(6 * y + 5d * y + d2 * y) = 0

Reorder the terms:
(5dy + d2y + 6y) = 0
(5dy + d2y + 6y) = 0

Solving
5dy + d2y + 6y = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(5d + d2 + 6) = 0

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

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(d + 2)' equal to zero and attempt to solve:

Simplifying
d + 2 = 0

Reorder the terms:
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 3
Set the factor '(d + 3)' equal to zero and attempt to solve:

Simplifying
d + 3 = 0

Reorder the terms:
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 = {-2, -3}