(h-6)(h+3)=0

Solution for (h-6)(h+3)=0 equation:

Simplifying
(h + -6)(h + 3) = 0

Reorder the terms:
(-6 + h)(h + 3) = 0

Reorder the terms:
(-6 + h)(3 + h) = 0

Multiply (-6 + h) * (3 + h)
(-6(3 + h) + h(3 + h)) = 0
((3 * -6 + h * -6) + h(3 + h)) = 0
((-18 + -6h) + h(3 + h)) = 0
(-18 + -6h + (3 * h + h * h)) = 0
(-18 + -6h + (3h + h2)) = 0

Combine like terms: -6h + 3h = -3h
(-18 + -3h + h2) = 0

Solving
-18 + -3h + h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-3 + -1h)(6 + -1h) = 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 '(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 = {-3, 6}