h(h+4)=3(h-2)+12

Solution for h(h+4)=3(h-2)+12 equation:

Simplifying
h(h + 4) = 3(h + -2) + 12

Reorder the terms:
h(4 + h) = 3(h + -2) + 12
(4 * h + h * h) = 3(h + -2) + 12
(4h + h2) = 3(h + -2) + 12

Reorder the terms:
4h + h2 = 3(-2 + h) + 12
4h + h2 = (-2 * 3 + h * 3) + 12
4h + h2 = (-6 + 3h) + 12

Reorder the terms:
4h + h2 = -6 + 12 + 3h

Combine like terms: -6 + 12 = 6
4h + h2 = 6 + 3h

Solving
4h + h2 = 6 + 3h

Solving for variable 'h'.

Reorder the terms:
-6 + 4h + -3h + h2 = 6 + 3h + -6 + -3h

Combine like terms: 4h + -3h = 1h
-6 + 1h + h2 = 6 + 3h + -6 + -3h

Reorder the terms:
-6 + 1h + h2 = 6 + -6 + 3h + -3h

Combine like terms: 6 + -6 = 0
-6 + 1h + h2 = 0 + 3h + -3h
-6 + 1h + h2 = 3h + -3h

Combine like terms: 3h + -3h = 0
-6 + 1h + h2 = 0

Factor a trinomial.
(-3 + -1h)(2 + -1h) = 0

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

Simplifying
-3 + -1h = 0

Solving
-3 + -1h = 0

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

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

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

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

Divide each side by '-1'.
h = -3

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

Simplifying
2 + -1h = 0

Solving
2 + -1h = 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 + -1h = 0 + -2

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

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

Divide each side by '-1'.
h = 2

Simplifying
h = 2
Solution
h = {-3, 2}