h(x+1)=h(x)+h(x-1)

Solution for h(x+1)=h(x)+h(x-1) equation:

Simplifying
h(x + 1) = h(x) + h(x + -1)

Reorder the terms:
h(1 + x) = h(x) + h(x + -1)
(1 * h + x * h) = h(x) + h(x + -1)
(1h + hx) = h(x) + h(x + -1)

Multiply h * x
1h + hx = hx + h(x + -1)

Reorder the terms:
1h + hx = hx + h(-1 + x)
1h + hx = hx + (-1 * h + x * h)
1h + hx = hx + (-1h + hx)

Reorder the terms:
1h + hx = -1h + hx + hx

Combine like terms: hx + hx = 2hx
1h + hx = -1h + 2hx

Solving
1h + hx = -1h + 2hx

Solving for variable 'h'.

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

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

Combine like terms: 1h + h = 2h
2h + hx = -1h + h + 2hx

Combine like terms: -1h + h = 0
2h + hx = 0 + 2hx
2h + hx = 2hx

Add '-2hx' to each side of the equation.
2h + hx + -2hx = 2hx + -2hx

Combine like terms: hx + -2hx = -1hx
2h + -1hx = 2hx + -2hx

Combine like terms: 2hx + -2hx = 0
2h + -1hx = 0

Factor out the Greatest Common Factor (GCF), 'h'.
h(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

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

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

Simplifying
0 = -2 + x

The solution to this equation could not be determined.

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