15x^2y-81xy^2+84y^3=0

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Solution for 15x^2y-81xy^2+84y^3=0 equation: 


Simplifying
15x2y + -81xy2 + 84y3 = 0

Reorder the terms:
-81xy2 + 15x2y + 84y3 = 0

Solving
-81xy2 + 15x2y + 84y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-27xy + 5x2 + 28y2) = 0

Factor a trinomial.
3y((x + -4y)(5x + -7y)) = 0

Ignore the factor 3.

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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(x + -4y)' equal to zero and attempt to solve:

Simplifying
x + -4y = 0

Solving
x + -4y = 0

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

Add '4y' to each side of the equation.
x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
x + 0 = 0 + 4y
x = 0 + 4y
Remove the zero:
x = 4y

Simplifying
x = 4y

Subproblem 3
Set the factor '(5x + -7y)' equal to zero and attempt to solve:

Simplifying
5x + -7y = 0

Solving
5x + -7y = 0

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

Add '7y' to each side of the equation.
5x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
5x + 0 = 0 + 7y
5x = 0 + 7y
Remove the zero:
5x = 7y

Divide each side by '5'.
x = 1.4y

Simplifying
x = 1.4y
Solution
x = {4y, 1.4y}

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