h^2-3h-54=0

Solution for h^2-3h-54=0 equation:

Simplifying
h2 + -3h + -54 = 0

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

Solving
-54 + -3h + h2 = 0

Solving for variable 'h'.

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

Subproblem 1
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
Subproblem 2
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
Solution
h = {-6, 9}