2y^6+7xy^3+6x^2=0

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Solution for 2y^6+7xy^3+6x^2=0 equation: 


Simplifying
2y6 + 7xy3 + 6x2 = 0

Reorder the terms:
7xy3 + 6x2 + 2y6 = 0

Solving
7xy3 + 6x2 + 2y6 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + y3)(3x + 2y3) = 0


Subproblem 1
Set the factor '(2x + y3)' equal to zero and attempt to solve:

Simplifying
2x + y3 = 0

Solving
2x + y3 = 0

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

Add '-1y3' to each side of the equation.
2x + y3 + -1y3 = 0 + -1y3

Combine like terms: y3 + -1y3 = 0
2x + 0 = 0 + -1y3
2x = 0 + -1y3
Remove the zero:
2x = -1y3

Divide each side by '2'.
x = -0.5y3

Simplifying
x = -0.5y3

Subproblem 2
Set the factor '(3x + 2y3)' equal to zero and attempt to solve:

Simplifying
3x + 2y3 = 0

Solving
3x + 2y3 = 0

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

Add '-2y3' to each side of the equation.
3x + 2y3 + -2y3 = 0 + -2y3

Combine like terms: 2y3 + -2y3 = 0
3x + 0 = 0 + -2y3
3x = 0 + -2y3
Remove the zero:
3x = -2y3

Divide each side by '3'.
x = -0.6666666667y3

Simplifying
x = -0.6666666667y3
Solution
x = {-0.5y3, -0.6666666667y3}

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