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

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

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

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

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

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

Combine like terms: -2h + 4h = 2h
(-1 + 2h + 8h2) = 0

Solving
-1 + 2h + 8h2 = 0

Solving for variable 'h'.

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

Subproblem 1
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
Subproblem 2
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
Solution
h = {-0.5, 0.25}