15x^4+27x^3y-6x^2y^2=0

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Solution for 15x^4+27x^3y-6x^2y^2=0 equation: 


Simplifying
15x4 + 27x3y + -6x2y2 = 0

Reorder the terms:
-6x2y2 + 27x3y + 15x4 = 0

Solving
-6x2y2 + 27x3y + 15x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-2y2 + 9xy + 5x2) = 0

Factor a trinomial.
3x2((-2y + -1x)(y + -5x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-2y + -1x)' equal to zero and attempt to solve:

Simplifying
-2y + -1x = 0

Reorder the terms:
-1x + -2y = 0

Solving
-1x + -2y = 0

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

Add '2y' to each side of the equation.
-1x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
-1x + 0 = 0 + 2y
-1x = 0 + 2y
Remove the zero:
-1x = 2y

Divide each side by '-1'.
x = -2y

Simplifying
x = -2y

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

Simplifying
y + -5x = 0

Reorder the terms:
-5x + y = 0

Solving
-5x + y = 0

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

Add '-1y' to each side of the equation.
-5x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-5x + 0 = 0 + -1y
-5x = 0 + -1y
Remove the zero:
-5x = -1y

Divide each side by '-5'.
x = 0.2y

Simplifying
x = 0.2y
Solution
x = {0, -2y, 0.2y}

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