0=2(h-7)(2h+3)

Solution for 0=2(h-7)(2h+3) equation:

Simplifying
0 = 2(h + -7)(2h + 3)

Reorder the terms:
0 = 2(-7 + h)(2h + 3)

Reorder the terms:
0 = 2(-7 + h)(3 + 2h)

Multiply (-7 + h) * (3 + 2h)
0 = 2(-7(3 + 2h) + h(3 + 2h))
0 = 2((3 * -7 + 2h * -7) + h(3 + 2h))
0 = 2((-21 + -14h) + h(3 + 2h))
0 = 2(-21 + -14h + (3 * h + 2h * h))
0 = 2(-21 + -14h + (3h + 2h2))

Combine like terms: -14h + 3h = -11h
0 = 2(-21 + -11h + 2h2)
0 = (-21 * 2 + -11h * 2 + 2h2 * 2)
0 = (-42 + -22h + 4h2)

Solving
0 = -42 + -22h + 4h2

Solving for variable 'h'.

Combine like terms: 0 + 42 = 42
42 + 22h + -4h2 = -42 + -22h + 4h2 + 42 + 22h + -4h2

Reorder the terms:
42 + 22h + -4h2 = -42 + 42 + -22h + 22h + 4h2 + -4h2

Combine like terms: -42 + 42 = 0
42 + 22h + -4h2 = 0 + -22h + 22h + 4h2 + -4h2
42 + 22h + -4h2 = -22h + 22h + 4h2 + -4h2

Combine like terms: -22h + 22h = 0
42 + 22h + -4h2 = 0 + 4h2 + -4h2
42 + 22h + -4h2 = 4h2 + -4h2

Combine like terms: 4h2 + -4h2 = 0
42 + 22h + -4h2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 11h + -2h2) = 0

Factor a trinomial.
2((7 + -1h)(3 + 2h)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -1h)' equal to zero and attempt to solve:

Simplifying
7 + -1h = 0

Solving
7 + -1h = 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 + -1h = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1h = 0 + -7
-1h = 0 + -7

Combine like terms: 0 + -7 = -7
-1h = -7

Divide each side by '-1'.
h = 7

Simplifying
h = 7
Subproblem 2
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
Solution
h = {7, -1.5}