(2h-1)(h+5)=0

Solution for (2h-1)(h+5)=0 equation:

Simplifying
(2h + -1)(h + 5) = 0

Reorder the terms:
(-1 + 2h)(h + 5) = 0

Reorder the terms:
(-1 + 2h)(5 + h) = 0

Multiply (-1 + 2h) * (5 + h)
(-1(5 + h) + 2h * (5 + h)) = 0
((5 * -1 + h * -1) + 2h * (5 + h)) = 0
((-5 + -1h) + 2h * (5 + h)) = 0
(-5 + -1h + (5 * 2h + h * 2h)) = 0
(-5 + -1h + (10h + 2h2)) = 0

Combine like terms: -1h + 10h = 9h
(-5 + 9h + 2h2) = 0

Solving
-5 + 9h + 2h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-5 + -1h)(1 + -2h) = 0

Subproblem 1
Set the factor '(-5 + -1h)' equal to zero and attempt to solve:

Simplifying
-5 + -1h = 0

Solving
-5 + -1h = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1h = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1h = 0 + 5
-1h = 0 + 5

Combine like terms: 0 + 5 = 5
-1h = 5

Divide each side by '-1'.
h = -5

Simplifying
h = -5
Subproblem 2
Set the factor '(1 + -2h)' equal to zero and attempt to solve:

Simplifying
1 + -2h = 0

Solving
1 + -2h = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2h = 0 + -1
-2h = 0 + -1

Combine like terms: 0 + -1 = -1
-2h = -1

Divide each side by '-2'.
h = 0.5

Simplifying
h = 0.5
Solution
h = {-5, 0.5}