2(h+1)(3h+1)=0

Solution for 2(h+1)(3h+1)=0 equation:

Simplifying
2(h + 1)(3h + 1) = 0

Reorder the terms:
2(1 + h)(3h + 1) = 0

Reorder the terms:
2(1 + h)(1 + 3h) = 0

Multiply (1 + h) * (1 + 3h)
2(1(1 + 3h) + h(1 + 3h)) = 0
2((1 * 1 + 3h * 1) + h(1 + 3h)) = 0
2((1 + 3h) + h(1 + 3h)) = 0
2(1 + 3h + (1 * h + 3h * h)) = 0
2(1 + 3h + (1h + 3h2)) = 0

Combine like terms: 3h + 1h = 4h
2(1 + 4h + 3h2) = 0
(1 * 2 + 4h * 2 + 3h2 * 2) = 0
(2 + 8h + 6h2) = 0

Solving
2 + 8h + 6h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 4h + 3h2) = 0

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

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

Simplifying
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 2
Set the factor '(1 + 3h)' equal to zero and attempt to solve:

Simplifying
1 + 3h = 0

Solving
1 + 3h = 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 + 3h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3h = 0 + -1
3h = 0 + -1

Combine like terms: 0 + -1 = -1
3h = -1

Divide each side by '3'.
h = -0.3333333333

Simplifying
h = -0.3333333333
Solution
h = {-1, -0.3333333333}