6h^2+17hk+10k^2=0

Solution for 6h^2+17hk+10k^2=0 equation:

Simplifying
6h2 + 17hk + 10k2 = 0

Reorder the terms:
17hk + 6h2 + 10k2 = 0

Solving
17hk + 6h2 + 10k2 = 0

Solving for variable 'h'.

Factor a trinomial.
(6h + 5k)(h + 2k) = 0

Subproblem 1
Set the factor '(6h + 5k)' equal to zero and attempt to solve:

Simplifying
6h + 5k = 0

Solving
6h + 5k = 0

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

Add '-5k' to each side of the equation.
6h + 5k + -5k = 0 + -5k

Combine like terms: 5k + -5k = 0
6h + 0 = 0 + -5k
6h = 0 + -5k
Remove the zero:
6h = -5k

Divide each side by '6'.
h = -0.8333333333k

Simplifying
h = -0.8333333333k
Subproblem 2
Set the factor '(h + 2k)' equal to zero and attempt to solve:

Simplifying
h + 2k = 0

Solving
h + 2k = 0

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

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

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

Simplifying
h = -2k
Solution
h = {-0.8333333333k, -2k}