(4h-7)(2h+1)=0

Solution for (4h-7)(2h+1)=0 equation:

Simplifying
(4h + -7)(2h + 1) = 0

Reorder the terms:
(-7 + 4h)(2h + 1) = 0

Reorder the terms:
(-7 + 4h)(1 + 2h) = 0

Multiply (-7 + 4h) * (1 + 2h)
(-7(1 + 2h) + 4h * (1 + 2h)) = 0
((1 * -7 + 2h * -7) + 4h * (1 + 2h)) = 0
((-7 + -14h) + 4h * (1 + 2h)) = 0
(-7 + -14h + (1 * 4h + 2h * 4h)) = 0
(-7 + -14h + (4h + 8h2)) = 0

Combine like terms: -14h + 4h = -10h
(-7 + -10h + 8h2) = 0

Solving
-7 + -10h + 8h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-1 + -2h)(7 + -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 '(7 + -4h)' equal to zero and attempt to solve:

Simplifying
7 + -4h = 0

Solving
7 + -4h = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4h = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4h = 0 + -7
-4h = 0 + -7

Combine like terms: 0 + -7 = -7
-4h = -7

Divide each side by '-4'.
h = 1.75

Simplifying
h = 1.75
Solution
h = {-0.5, 1.75}