(2h-8)(4h+1)=0

Solution for (2h-8)(4h+1)=0 equation:

Simplifying
(2h + -8)(4h + 1) = 0

Reorder the terms:
(-8 + 2h)(4h + 1) = 0

Reorder the terms:
(-8 + 2h)(1 + 4h) = 0

Multiply (-8 + 2h) * (1 + 4h)
(-8(1 + 4h) + 2h * (1 + 4h)) = 0
((1 * -8 + 4h * -8) + 2h * (1 + 4h)) = 0
((-8 + -32h) + 2h * (1 + 4h)) = 0
(-8 + -32h + (1 * 2h + 4h * 2h)) = 0
(-8 + -32h + (2h + 8h2)) = 0

Combine like terms: -32h + 2h = -30h
(-8 + -30h + 8h2) = 0

Solving
-8 + -30h + 8h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -15h + 4h2) = 0

Factor a trinomial.
2((-1 + -4h)(4 + -1h)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -4h)' equal to zero and attempt to solve:

Simplifying
-1 + -4h = 0

Solving
-1 + -4h = 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 + -4h = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4h = 0 + 1
-4h = 0 + 1

Combine like terms: 0 + 1 = 1
-4h = 1

Divide each side by '-4'.
h = -0.25

Simplifying
h = -0.25
Subproblem 2
Set the factor '(4 + -1h)' equal to zero and attempt to solve:

Simplifying
4 + -1h = 0

Solving
4 + -1h = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1h = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1h = 0 + -4
-1h = 0 + -4

Combine like terms: 0 + -4 = -4
-1h = -4

Divide each side by '-1'.
h = 4

Simplifying
h = 4
Solution
h = {-0.25, 4}