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

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

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

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

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

Reorder the terms for easier multiplication:
h(1 + 3h)(-3 + 2h) = 0

Multiply (1 + 3h) * (-3 + 2h)
h(1(-3 + 2h) + 3h * (-3 + 2h)) = 0
h((-3 * 1 + 2h * 1) + 3h * (-3 + 2h)) = 0
h((-3 + 2h) + 3h * (-3 + 2h)) = 0
h(-3 + 2h + (-3 * 3h + 2h * 3h)) = 0
h(-3 + 2h + (-9h + 6h2)) = 0

Combine like terms: 2h + -9h = -7h
h(-3 + -7h + 6h2) = 0
(-3 * h + -7h * h + 6h2 * h) = 0
(-3h + -7h2 + 6h3) = 0

Solving
-3h + -7h2 + 6h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), 'h'.
h(-3 + -7h + 6h2) = 0

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

Subproblem 1
Set the factor 'h' equal to zero and attempt to solve:

Simplifying
h = 0

Solving
h = 0

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

Simplifying
h = 0
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
Subproblem 3
Set the factor '(3 + -2h)' equal to zero and attempt to solve:

Simplifying
3 + -2h = 0

Solving
3 + -2h = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2h = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2h = 0 + -3
-2h = 0 + -3

Combine like terms: 0 + -3 = -3
-2h = -3

Divide each side by '-2'.
h = 1.5

Simplifying
h = 1.5
Solution
h = {0, -0.3333333333, 1.5}