3h(h-4)(3h+2)=0

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Solution for 3h(h-4)(3h+2)=0 equation: 


Simplifying
3h(h + -4)(3h + 2) = 0

Reorder the terms:
3h(-4 + h)(3h + 2) = 0

Reorder the terms:
3h(-4 + h)(2 + 3h) = 0

Multiply (-4 + h) * (2 + 3h)
3h(-4(2 + 3h) + h(2 + 3h)) = 0
3h((2 * -4 + 3h * -4) + h(2 + 3h)) = 0
3h((-8 + -12h) + h(2 + 3h)) = 0
3h(-8 + -12h + (2 * h + 3h * h)) = 0
3h(-8 + -12h + (2h + 3h2)) = 0

Combine like terms: -12h + 2h = -10h
3h(-8 + -10h + 3h2) = 0
(-8 * 3h + -10h * 3h + 3h2 * 3h) = 0
(-24h + -30h2 + 9h3) = 0

Solving
-24h + -30h2 + 9h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3h'.
3h(-8 + -10h + 3h2) = 0

Factor a trinomial.
3h((-2 + -3h)(4 + -1h)) = 0

Ignore the factor 3.

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 '(-2 + -3h)' equal to zero and attempt to solve:

Simplifying
-2 + -3h = 0

Solving
-2 + -3h = 0

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

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

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

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

Divide each side by '-3'.
h = -0.6666666667

Simplifying
h = -0.6666666667

Subproblem 3
Set the factor '(4 + -1h)' equal to zero and attempt to solve:

Simplifying
4 + -1h = 0

Solving
4 + -1h = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1h = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1h = 0 + -4
-1h = 0 + -4

Combine like terms: 0 + -4 = -4
-1h = -4

Divide each side by '-1'.
h = 4

Simplifying
h = 4
Solution
h = {0, -0.6666666667, 4}

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