180x^2y-108xy^2-75x^3=0

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Solution for 180x^2y-108xy^2-75x^3=0 equation: 


Simplifying
180x2y + -108xy2 + -75x3 = 0

Reorder the terms:
-108xy2 + 180x2y + -75x3 = 0

Solving
-108xy2 + 180x2y + -75x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-36y2 + 60xy + -25x2) = 0

Factor a trinomial.
3x((-6y + 5x)(6y + -5x)) = 0

Ignore the factor 3.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-6y + 5x)' equal to zero and attempt to solve:

Simplifying
-6y + 5x = 0

Reorder the terms:
5x + -6y = 0

Solving
5x + -6y = 0

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

Add '6y' to each side of the equation.
5x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
5x + 0 = 0 + 6y
5x = 0 + 6y
Remove the zero:
5x = 6y

Divide each side by '5'.
x = 1.2y

Simplifying
x = 1.2y

Subproblem 3
Set the factor '(6y + -5x)' equal to zero and attempt to solve:

Simplifying
6y + -5x = 0

Reorder the terms:
-5x + 6y = 0

Solving
-5x + 6y = 0

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

Add '-6y' to each side of the equation.
-5x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
-5x + 0 = 0 + -6y
-5x = 0 + -6y
Remove the zero:
-5x = -6y

Divide each side by '-5'.
x = 1.2y

Simplifying
x = 1.2y
Solution
x = {0, 1.2y, 1.2y}

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