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

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

Simplifying
(2h + 3)(2 + 3h + 4) = 0

Reorder the terms:
(3 + 2h)(2 + 3h + 4) = 0

Reorder the terms:
(3 + 2h)(2 + 4 + 3h) = 0

Combine like terms: 2 + 4 = 6
(3 + 2h)(6 + 3h) = 0

Multiply (3 + 2h) * (6 + 3h)
(3(6 + 3h) + 2h * (6 + 3h)) = 0
((6 * 3 + 3h * 3) + 2h * (6 + 3h)) = 0
((18 + 9h) + 2h * (6 + 3h)) = 0
(18 + 9h + (6 * 2h + 3h * 2h)) = 0
(18 + 9h + (12h + 6h2)) = 0

Combine like terms: 9h + 12h = 21h
(18 + 21h + 6h2) = 0

Solving
18 + 21h + 6h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 7h + 2h2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + h)' equal to zero and attempt to solve:

Simplifying
2 + h = 0

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

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

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

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

Simplifying
3 + 2h = 0

Solving
3 + 2h = 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 + 2h = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2h = 0 + -3
2h = 0 + -3

Combine like terms: 0 + -3 = -3
2h = -3

Divide each side by '2'.
h = -1.5

Simplifying
h = -1.5
Solution
h = {-2, -1.5}