(4x+8y^2)(x-y^2)=0

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Solution for (4x+8y^2)(x-y^2)=0 equation: 


Simplifying
(4x + 8y2)(x + -1y2) = 0

Multiply (4x + 8y2) * (x + -1y2)
(4x * (x + -1y2) + 8y2 * (x + -1y2)) = 0
((x * 4x + -1y2 * 4x) + 8y2 * (x + -1y2)) = 0

Reorder the terms:
((-4xy2 + 4x2) + 8y2 * (x + -1y2)) = 0
((-4xy2 + 4x2) + 8y2 * (x + -1y2)) = 0
(-4xy2 + 4x2 + (x * 8y2 + -1y2 * 8y2)) = 0
(-4xy2 + 4x2 + (8xy2 + -8y4)) = 0

Reorder the terms:
(-4xy2 + 8xy2 + 4x2 + -8y4) = 0

Combine like terms: -4xy2 + 8xy2 = 4xy2
(4xy2 + 4x2 + -8y4) = 0

Solving
4xy2 + 4x2 + -8y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(xy2 + x2 + -2y4) = 0

Factor a trinomial.
4((x + -1y2)(x + 2y2)) = 0

Ignore the factor 4.

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 '(x + 2y2)' equal to zero and attempt to solve:

Simplifying
x + 2y2 = 0

Solving
x + 2y2 = 0

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

Add '-2y2' to each side of the equation.
x + 2y2 + -2y2 = 0 + -2y2

Combine like terms: 2y2 + -2y2 = 0
x + 0 = 0 + -2y2
x = 0 + -2y2
Remove the zero:
x = -2y2

Simplifying
x = -2y2
Solution
x = {y2, -2y2}

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