2h(4h+7)=15

Solution for 2h(4h+7)=15 equation:

Simplifying
2h(4h + 7) = 15

Reorder the terms:
2h(7 + 4h) = 15
(7 * 2h + 4h * 2h) = 15
(14h + 8h2) = 15

Solving
14h + 8h2 = 15

Solving for variable 'h'.

Reorder the terms:
-15 + 14h + 8h2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 14h + 8h2 = 0

Factor a trinomial.
(-5 + -2h)(3 + -4h) = 0

Subproblem 1
Set the factor '(-5 + -2h)' equal to zero and attempt to solve:

Simplifying
-5 + -2h = 0

Solving
-5 + -2h = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2h = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2h = 0 + 5
-2h = 0 + 5

Combine like terms: 0 + 5 = 5
-2h = 5

Divide each side by '-2'.
h = -2.5

Simplifying
h = -2.5
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 = {-2.5, 0.75}