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

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


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

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

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

Solving for variable 'x'.

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

Factor a trinomial.
3x2((-5y + -1x)(y + -2x)) = 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 '(-5y + -1x)' equal to zero and attempt to solve:

Simplifying
-5y + -1x = 0

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

Solving
-1x + -5y = 0

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

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

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

Divide each side by '-1'.
x = -5y

Simplifying
x = -5y

Subproblem 3
Set the factor '(y + -2x)' equal to zero and attempt to solve:

Simplifying
y + -2x = 0

Reorder the terms:
-2x + y = 0

Solving
-2x + y = 0

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

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

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

Divide each side by '-2'.
x = 0.5y

Simplifying
x = 0.5y
Solution
x = {0, -5y, 0.5y}

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