h(h+1)(h+4)=0

Solution for h(h+1)(h+4)=0 equation:

Simplifying
h(h + 1)(h + 4) = 0

Reorder the terms:
h(1 + h)(h + 4) = 0

Reorder the terms:
h(1 + h)(4 + h) = 0

Multiply (1 + h) * (4 + h)
h(1(4 + h) + h(4 + h)) = 0
h((4 * 1 + h * 1) + h(4 + h)) = 0
h((4 + 1h) + h(4 + h)) = 0
h(4 + 1h + (4 * h + h * h)) = 0
h(4 + 1h + (4h + h2)) = 0

Combine like terms: 1h + 4h = 5h
h(4 + 5h + h2) = 0
(4 * h + 5h * h + h2 * h) = 0
(4h + 5h2 + h3) = 0

Solving
4h + 5h2 + h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), 'h'.
h(4 + 5h + h2) = 0

Factor a trinomial.
h((4 + h)(1 + h)) = 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 '(4 + h)' equal to zero and attempt to solve:

Simplifying
4 + h = 0

Solving
4 + h = 0

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

Add '-4' to each side of the equation.
4 + -4 + h = 0 + -4

Combine like terms: 4 + -4 = 0
0 + h = 0 + -4
h = 0 + -4

Combine like terms: 0 + -4 = -4
h = -4

Simplifying
h = -4
Subproblem 3
Set the factor '(1 + h)' equal to zero and attempt to solve:

Simplifying
1 + h = 0

Solving
1 + h = 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 + h = 0 + -1

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

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

Simplifying
h = -1
Solution
h = {0, -4, -1}