(h+3)(h)-54=0

Solution for (h+3)(h)-54=0 equation:

Simplifying
(h + 3)(h) + -54 = 0

Reorder the terms:
(3 + h)(h) + -54 = 0

Reorder the terms for easier multiplication:
h(3 + h) + -54 = 0
(3 * h + h * h) + -54 = 0
(3h + h2) + -54 = 0

Reorder the terms:
-54 + 3h + h2 = 0

Solving
-54 + 3h + h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-9 + -1h)(6 + -1h) = 0

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

Simplifying
-9 + -1h = 0

Solving
-9 + -1h = 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 + -1h = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1h = 0 + 9
-1h = 0 + 9

Combine like terms: 0 + 9 = 9
-1h = 9

Divide each side by '-1'.
h = -9

Simplifying
h = -9
Subproblem 2
Set the factor '(6 + -1h)' equal to zero and attempt to solve:

Simplifying
6 + -1h = 0

Solving
6 + -1h = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1h = 0 + -6

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

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

Divide each side by '-1'.
h = 6

Simplifying
h = 6
Solution
h = {-9, 6}