(2h+3)(h)=27

Solution for (2h+3)(h)=27 equation:

Simplifying
(2h + 3)(h) = 27

Reorder the terms:
(3 + 2h)(h) = 27

Reorder the terms for easier multiplication:
h(3 + 2h) = 27
(3 * h + 2h * h) = 27
(3h + 2h2) = 27

Solving
3h + 2h2 = 27

Solving for variable 'h'.

Reorder the terms:
-27 + 3h + 2h2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 3h + 2h2 = 0

Factor a trinomial.
(-9 + -2h)(3 + -1h) = 0

Subproblem 1
Set the factor '(-9 + -2h)' equal to zero and attempt to solve:

Simplifying
-9 + -2h = 0

Solving
-9 + -2h = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2h = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2h = 0 + 9
-2h = 0 + 9

Combine like terms: 0 + 9 = 9
-2h = 9

Divide each side by '-2'.
h = -4.5

Simplifying
h = -4.5
Subproblem 2
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
Solution
h = {-4.5, 3}