(6x+y^2)(x-y^2)=0

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Solution for (6x+y^2)(x-y^2)=0 equation: 


Simplifying
(6x + y2)(x + -1y2) = 0

Multiply (6x + y2) * (x + -1y2)
(6x * (x + -1y2) + y2(x + -1y2)) = 0
((x * 6x + -1y2 * 6x) + y2(x + -1y2)) = 0

Reorder the terms:
((-6xy2 + 6x2) + y2(x + -1y2)) = 0
((-6xy2 + 6x2) + y2(x + -1y2)) = 0
(-6xy2 + 6x2 + (x * y2 + -1y2 * y2)) = 0
(-6xy2 + 6x2 + (xy2 + -1y4)) = 0

Reorder the terms:
(-6xy2 + xy2 + 6x2 + -1y4) = 0

Combine like terms: -6xy2 + xy2 = -5xy2
(-5xy2 + 6x2 + -1y4) = 0

Solving
-5xy2 + 6x2 + -1y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y2)(6x + y2) = 0


Subproblem 1
Set the factor '(x + -1y2)' equal to zero and attempt to solve:

Simplifying
x + -1y2 = 0

Solving
x + -1y2 = 0

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

Add 'y2' to each side of the equation.
x + -1y2 + y2 = 0 + y2

Combine like terms: -1y2 + y2 = 0
x + 0 = 0 + y2
x = 0 + y2
Remove the zero:
x = y2

Simplifying
x = y2

Subproblem 2
Set the factor '(6x + y2)' equal to zero and attempt to solve:

Simplifying
6x + y2 = 0

Solving
6x + y2 = 0

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

Add '-1y2' to each side of the equation.
6x + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
6x + 0 = 0 + -1y2
6x = 0 + -1y2
Remove the zero:
6x = -1y2

Divide each side by '6'.
x = -0.1666666667y2

Simplifying
x = -0.1666666667y2
Solution
x = {y2, -0.1666666667y2}

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