(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
(-6y + 5yD + yD2) = 0

Solving
-6y + 5yD + 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 + 5D + D2) = 0

Factor a trinomial.
y((-6 + -1D)(1 + -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 '(-6 + -1D)' equal to zero and attempt to solve:

Simplifying
-6 + -1D = 0

Solving
-6 + -1D = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1D = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1D = 0 + 6
-1D = 0 + 6

Combine like terms: 0 + 6 = 6
-1D = 6

Add 'D' to each side of the equation.
-1D + D = 6 + D

Combine like terms: -1D + D = 0
0 = 6 + D

Simplifying
0 = 6 + 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 '(1 + -1D)' equal to zero and attempt to solve:

Simplifying
1 + -1D = 0

Solving
1 + -1D = 0

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

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

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

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

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

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

Simplifying
0 = -1 + 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}