(2h+9)(4h-3)=0

Solution for (2h+9)(4h-3)=0 equation:

Simplifying
(2h + 9)(4h + -3) = 0

Reorder the terms:
(9 + 2h)(4h + -3) = 0

Reorder the terms:
(9 + 2h)(-3 + 4h) = 0

Multiply (9 + 2h) * (-3 + 4h)
(9(-3 + 4h) + 2h * (-3 + 4h)) = 0
((-3 * 9 + 4h * 9) + 2h * (-3 + 4h)) = 0
((-27 + 36h) + 2h * (-3 + 4h)) = 0
(-27 + 36h + (-3 * 2h + 4h * 2h)) = 0
(-27 + 36h + (-6h + 8h2)) = 0

Combine like terms: 36h + -6h = 30h
(-27 + 30h + 8h2) = 0

Solving
-27 + 30h + 8h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-9 + -2h)(3 + -4h) = 0

Subproblem 1
Set the factor '(-9 + -2h)' equal to zero and attempt to solve:

Simplifying
-9 + -2h = 0

Solving
-9 + -2h = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2h = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2h = 0 + 9
-2h = 0 + 9

Combine like terms: 0 + 9 = 9
-2h = 9

Divide each side by '-2'.
h = -4.5

Simplifying
h = -4.5
Subproblem 2
Set the factor '(3 + -4h)' equal to zero and attempt to solve:

Simplifying
3 + -4h = 0

Solving
3 + -4h = 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 + -4h = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4h = 0 + -3
-4h = 0 + -3

Combine like terms: 0 + -3 = -3
-4h = -3

Divide each side by '-4'.
h = 0.75

Simplifying
h = 0.75
Solution
h = {-4.5, 0.75}