(4h-1)(2h+3)=0

Solution for (4h-1)(2h+3)=0 equation:

Simplifying
(4h + -1)(2h + 3) = 0

Reorder the terms:
(-1 + 4h)(2h + 3) = 0

Reorder the terms:
(-1 + 4h)(3 + 2h) = 0

Multiply (-1 + 4h) * (3 + 2h)
(-1(3 + 2h) + 4h * (3 + 2h)) = 0
((3 * -1 + 2h * -1) + 4h * (3 + 2h)) = 0
((-3 + -2h) + 4h * (3 + 2h)) = 0
(-3 + -2h + (3 * 4h + 2h * 4h)) = 0
(-3 + -2h + (12h + 8h2)) = 0

Combine like terms: -2h + 12h = 10h
(-3 + 10h + 8h2) = 0

Solving
-3 + 10h + 8h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-3 + -2h)(1 + -4h) = 0

Subproblem 1
Set the factor '(-3 + -2h)' equal to zero and attempt to solve:

Simplifying
-3 + -2h = 0

Solving
-3 + -2h = 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 + -2h = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2h = 0 + 3
-2h = 0 + 3

Combine like terms: 0 + 3 = 3
-2h = 3

Divide each side by '-2'.
h = -1.5

Simplifying
h = -1.5
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 = {-1.5, 0.25}