(3h+12)(h+1)=0

Solution for (3h+12)(h+1)=0 equation:

Simplifying
(3h + 12)(h + 1) = 0

Reorder the terms:
(12 + 3h)(h + 1) = 0

Reorder the terms:
(12 + 3h)(1 + h) = 0

Multiply (12 + 3h) * (1 + h)
(12(1 + h) + 3h * (1 + h)) = 0
((1 * 12 + h * 12) + 3h * (1 + h)) = 0
((12 + 12h) + 3h * (1 + h)) = 0
(12 + 12h + (1 * 3h + h * 3h)) = 0
(12 + 12h + (3h + 3h2)) = 0

Combine like terms: 12h + 3h = 15h
(12 + 15h + 3h2) = 0

Solving
12 + 15h + 3h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 5h + h2) = 0

Factor a trinomial.
3((4 + h)(1 + h)) = 0

Ignore the factor 3.
Subproblem 1
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 2
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 = {-4, -1}