-75h^3+90h^2y-27hy^2=0

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Solution for -75h^3+90h^2y-27hy^2=0 equation: 


Simplifying
-75h3 + 90h2y + -27hy2 = 0

Reorder the terms:
-27hy2 + 90h2y + -75h3 = 0

Solving
-27hy2 + 90h2y + -75h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3h'.
3h(-9y2 + 30hy + -25h2) = 0

Factor a trinomial.
3h((-3y + 5h)(3y + -5h)) = 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 '(-3y + 5h)' equal to zero and attempt to solve:

Simplifying
-3y + 5h = 0

Reorder the terms:
5h + -3y = 0

Solving
5h + -3y = 0

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

Add '3y' to each side of the equation.
5h + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
5h + 0 = 0 + 3y
5h = 0 + 3y
Remove the zero:
5h = 3y

Divide each side by '5'.
h = 0.6y

Simplifying
h = 0.6y

Subproblem 3
Set the factor '(3y + -5h)' equal to zero and attempt to solve:

Simplifying
3y + -5h = 0

Reorder the terms:
-5h + 3y = 0

Solving
-5h + 3y = 0

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

Add '-3y' to each side of the equation.
-5h + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-5h + 0 = 0 + -3y
-5h = 0 + -3y
Remove the zero:
-5h = -3y

Divide each side by '-5'.
h = 0.6y

Simplifying
h = 0.6y
Solution
h = {0, 0.6y, 0.6y}

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