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((-1y + -5x)(2y + -1x)) = 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 '(-1y + -5x)' equal to zero and attempt to solve:

Simplifying
-1y + -5x = 0

Reorder the terms:
-5x + -1y = 0

Solving
-5x + -1y = 0

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

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

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

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

Simplifying
x = -0.2y

Subproblem 3
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
Solution
x = {0, -0.2y, 2y}

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