27=h(2h+3)

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

Simplifying
27 = h(2h + 3)

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

Solving
27 = 3h + 2h2

Solving for variable 'h'.

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

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

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

Factor a trinomial.
(3 + -1h)(9 + 2h) = 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 '(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
Solution
h = {3, -4.5}