(D^2+D-6)y=0

Solution for (D^2+D-6)y=0 equation:

Simplifying
(D2 + D + -6) * y = 0

Reorder the terms:
(-6 + D + D2) * y = 0

Reorder the terms for easier multiplication:
y(-6 + D + D2) = 0
(-6 * y + D * y + D2 * y) = 0
(-6y + yD + yD2) = 0

Solving
-6y + yD + yD2 = 0

Solving for variable 'y'.

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

Factor out the Greatest Common Factor (GCF), 'y'.
y(-6 + D + D2) = 0

Factor a trinomial.
y((-3 + -1D)(2 + -1D)) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
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 y 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

Add 'D' to each side of the equation.
-1D + D = 3 + D

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

Simplifying
0 = 3 + D

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(2 + -1D)' equal to zero and attempt to solve:

Simplifying
2 + -1D = 0

Solving
2 + -1D = 0

Move all terms containing y 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

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

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

Simplifying
0 = -2 + D

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}