-48h^3+72h^2-27h=0

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Solution for -48h^3+72h^2-27h=0 equation:


Simplifying
-48h3 + 72h2 + -27h = 0

Reorder the terms:
-27h + 72h2 + -48h3 = 0

Solving
-27h + 72h2 + -48h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3h'.
3h(-9 + 24h + -16h2) = 0

Factor a trinomial.
3h((-3 + 4h)(3 + -4h)) = 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 '(-3 + 4h)' equal to zero and attempt to solve: Simplifying -3 + 4h = 0 Solving -3 + 4h = 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 + 4h = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4h = 0 + 3 4h = 0 + 3 Combine like terms: 0 + 3 = 3 4h = 3 Divide each side by '4'. h = 0.75 Simplifying h = 0.75

Subproblem 3

Set the factor '(3 + -4h)' equal to zero and attempt to solve: Simplifying 3 + -4h = 0 Solving 3 + -4h = 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 + -4h = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4h = 0 + -3 -4h = 0 + -3 Combine like terms: 0 + -3 = -3 -4h = -3 Divide each side by '-4'. h = 0.75 Simplifying h = 0.75

Solution

h = {0, 0.75, 0.75}

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