H(y+1)-H(y)=3H(y)

Solution for H(y+1)-H(y)=3H(y) equation:

Simplifying
H(y + 1) + -1H(y) = 3H(y)

Reorder the terms:
H(1 + y) + -1H(y) = 3H(y)
(1 * H + y * H) + -1H(y) = 3H(y)
(1H + yH) + -1H(y) = 3H(y)

Multiply H * y
1H + yH + -1yH = 3H(y)

Combine like terms: yH + -1yH = 0
1H + 0 = 3H(y)
1H = 3H(y)

Multiply H * y
1H = 3yH

Solving
1H = 3yH

Solving for variable 'H'.

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

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

Combine like terms: 3yH + -3yH = 0
1H + -3yH = 0

Factor out the Greatest Common Factor (GCF), 'H'.
H(1 + -3y) = 0

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

Simplifying
H = 0

Solving
H = 0

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

Simplifying
H = 0
Subproblem 2
Set the factor '(1 + -3y)' equal to zero and attempt to solve:

Simplifying
1 + -3y = 0

Solving
1 + -3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3y = 0 + -1

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

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

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

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

Simplifying
0 = -1 + 3y

The solution to this equation could not be determined.

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