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

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


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

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

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

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

Combine like terms: -1xy2 + -6xy2 = -7xy2
(-7xy2 + 6x2 + 1y4) = 0

Solving
-7xy2 + 6x2 + 1y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y2)(6x + -1y2) = 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 + -1y2)' equal to zero and attempt to solve:

Simplifying
6x + -1y2 = 0

Solving
6x + -1y2 = 0

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

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

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

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

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

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