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

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


Simplifying
(4x + -1y2)(x + 2y2) = 0

Multiply (4x + -1y2) * (x + 2y2)
(4x * (x + 2y2) + -1y2 * (x + 2y2)) = 0
((x * 4x + 2y2 * 4x) + -1y2 * (x + 2y2)) = 0

Reorder the terms:
((8xy2 + 4x2) + -1y2 * (x + 2y2)) = 0
((8xy2 + 4x2) + -1y2 * (x + 2y2)) = 0
(8xy2 + 4x2 + (x * -1y2 + 2y2 * -1y2)) = 0
(8xy2 + 4x2 + (-1xy2 + -2y4)) = 0

Reorder the terms:
(8xy2 + -1xy2 + 4x2 + -2y4) = 0

Combine like terms: 8xy2 + -1xy2 = 7xy2
(7xy2 + 4x2 + -2y4) = 0

Solving
7xy2 + 4x2 + -2y4 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(4x + -1y2)' equal to zero and attempt to solve:

Simplifying
4x + -1y2 = 0

Solving
4x + -1y2 = 0

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

Add 'y2' to each side of the equation.
4x + -1y2 + y2 = 0 + y2

Combine like terms: -1y2 + y2 = 0
4x + 0 = 0 + y2
4x = 0 + y2
Remove the zero:
4x = y2

Divide each side by '4'.
x = 0.25y2

Simplifying
x = 0.25y2

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 = {0.25y2, -2y2}

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