(2h+4k)(3h-k)-5hk=

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Solution for (2h+4k)(3h-k)-5hk= equation: 


Simplifying
(2h + 4k)(3h + -1k) + -5hk = 0

Multiply (2h + 4k) * (3h + -1k)
(2h * (3h + -1k) + 4k * (3h + -1k)) + -5hk = 0
((3h * 2h + -1k * 2h) + 4k * (3h + -1k)) + -5hk = 0

Reorder the terms:
((-2hk + 6h2) + 4k * (3h + -1k)) + -5hk = 0
((-2hk + 6h2) + 4k * (3h + -1k)) + -5hk = 0
(-2hk + 6h2 + (3h * 4k + -1k * 4k)) + -5hk = 0
(-2hk + 6h2 + (12hk + -4k2)) + -5hk = 0

Reorder the terms:
(-2hk + 12hk + 6h2 + -4k2) + -5hk = 0

Combine like terms: -2hk + 12hk = 10hk
(10hk + 6h2 + -4k2) + -5hk = 0

Reorder the terms:
10hk + -5hk + 6h2 + -4k2 = 0

Combine like terms: 10hk + -5hk = 5hk
5hk + 6h2 + -4k2 = 0

Solving
5hk + 6h2 + -4k2 = 0

Solving for variable 'h'.

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


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

Simplifying
2h + -1k = 0

Solving
2h + -1k = 0

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

Add 'k' to each side of the equation.
2h + -1k + k = 0 + k

Combine like terms: -1k + k = 0
2h + 0 = 0 + k
2h = 0 + k
Remove the zero:
2h = k

Divide each side by '2'.
h = 0.5k

Simplifying
h = 0.5k

Subproblem 2
Set the factor '(3h + 4k)' equal to zero and attempt to solve:

Simplifying
3h + 4k = 0

Solving
3h + 4k = 0

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

Add '-4k' to each side of the equation.
3h + 4k + -4k = 0 + -4k

Combine like terms: 4k + -4k = 0
3h + 0 = 0 + -4k
3h = 0 + -4k
Remove the zero:
3h = -4k

Divide each side by '3'.
h = -1.333333333k

Simplifying
h = -1.333333333k
Solution
h = {0.5k, -1.333333333k}

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