-36h^3+120h^2y-100hy^2=0

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Solution for -36h^3+120h^2y-100hy^2=0 equation:


Simplifying
-36h3 + 120h2y + -100hy2 = 0

Reorder the terms:
-100hy2 + 120h2y + -36h3 = 0

Solving
-100hy2 + 120h2y + -36h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4h'.
4h(-25y2 + 30hy + -9h2) = 0

Factor a trinomial.
4h((-5y + 3h)(5y + -3h)) = 0

Ignore the factor 4.

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 '(-5y + 3h)' equal to zero and attempt to solve: Simplifying -5y + 3h = 0 Reorder the terms: 3h + -5y = 0 Solving 3h + -5y = 0 Move all terms containing h to the left, all other terms to the right. Add '5y' to each side of the equation. 3h + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 3h + 0 = 0 + 5y 3h = 0 + 5y Remove the zero: 3h = 5y Divide each side by '3'. h = 1.666666667y Simplifying h = 1.666666667y

Subproblem 3

Set the factor '(5y + -3h)' equal to zero and attempt to solve: Simplifying 5y + -3h = 0 Reorder the terms: -3h + 5y = 0 Solving -3h + 5y = 0 Move all terms containing h to the left, all other terms to the right. Add '-5y' to each side of the equation. -3h + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 -3h + 0 = 0 + -5y -3h = 0 + -5y Remove the zero: -3h = -5y Divide each side by '-3'. h = 1.666666667y Simplifying h = 1.666666667y

Solution

h = {0, 1.666666667y, 1.666666667y}

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