h^2(3t+6)=3t-3

Solution for h^2(3t+6)=3t-3 equation:

Simplifying
h2(3t + 6) = 3t + -3

Reorder the terms:
h2(6 + 3t) = 3t + -3
(6 * h2 + 3t * h2) = 3t + -3
(6h2 + 3h2t) = 3t + -3

Reorder the terms:
6h2 + 3h2t = -3 + 3t

Solving
6h2 + 3h2t = -3 + 3t

Solving for variable 'h'.

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

Reorder the terms:
3 + 6h2 + 3h2t + -3t = -3 + 3t + 3 + -3t

Reorder the terms:
3 + 6h2 + 3h2t + -3t = -3 + 3 + 3t + -3t

Combine like terms: -3 + 3 = 0
3 + 6h2 + 3h2t + -3t = 0 + 3t + -3t
3 + 6h2 + 3h2t + -3t = 3t + -3t

Combine like terms: 3t + -3t = 0
3 + 6h2 + 3h2t + -3t = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 2h2 + h2t + -1t) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 2h2 + h2t + -1t)' equal to zero and attempt to solve:

Simplifying
1 + 2h2 + h2t + -1t = 0

Solving
1 + 2h2 + h2t + -1t = 0

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

Add '-1' to each side of the equation.
1 + 2h2 + h2t + -1 + -1t = 0 + -1

Reorder the terms:
1 + -1 + 2h2 + h2t + -1t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2h2 + h2t + -1t = 0 + -1
2h2 + h2t + -1t = 0 + -1

Combine like terms: 0 + -1 = -1
2h2 + h2t + -1t = -1

Add 't' to each side of the equation.
2h2 + h2t + -1t + t = -1 + t

Combine like terms: -1t + t = 0
2h2 + h2t + 0 = -1 + t
2h2 + h2t = -1 + t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.