3h^2t+6ht+3t=0

Solution for 3h^2t+6ht+3t=0 equation:

Simplifying
3h2t + 6ht + 3t = 0

Reorder the terms:
6ht + 3h2t + 3t = 0

Solving
6ht + 3h2t + 3t = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3t'.
3t(2h + h2 + 1) = 0

Factor a trinomial.
3t((h + 1)(h + 1)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Add '-1t' to each side of the equation.
t + -1t = 0 + -1t
Remove the zero:
0 = -1t

Simplifying
0 = -1t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(h + 1)' equal to zero and attempt to solve:

Simplifying
h + 1 = 0

Reorder the terms:
1 + h = 0

Solving
1 + h = 0

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

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

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

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

Simplifying
h = -1
Subproblem 3
Set the factor '(h + 1)' equal to zero and attempt to solve:

Simplifying
h + 1 = 0

Reorder the terms:
1 + h = 0

Solving
1 + h = 0

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

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

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

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

Simplifying
h = -1
Solution
h = {-1, -1}