(4x^2-y^2)(x^2+5y^2)=

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Solution for (4x^2-y^2)(x^2+5y^2)= equation: 


Simplifying
(4x2 + -1y2)(x2 + 5y2) = 0

Multiply (4x2 + -1y2) * (x2 + 5y2)
(4x2 * (x2 + 5y2) + -1y2 * (x2 + 5y2)) = 0
((x2 * 4x2 + 5y2 * 4x2) + -1y2 * (x2 + 5y2)) = 0

Reorder the terms:
((20x2y2 + 4x4) + -1y2 * (x2 + 5y2)) = 0
((20x2y2 + 4x4) + -1y2 * (x2 + 5y2)) = 0
(20x2y2 + 4x4 + (x2 * -1y2 + 5y2 * -1y2)) = 0
(20x2y2 + 4x4 + (-1x2y2 + -5y4)) = 0

Reorder the terms:
(20x2y2 + -1x2y2 + 4x4 + -5y4) = 0

Combine like terms: 20x2y2 + -1x2y2 = 19x2y2
(19x2y2 + 4x4 + -5y4) = 0

Solving
19x2y2 + 4x4 + -5y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x2 + -1y2)(x2 + 5y2) = 0

Factor a difference between two squares.
((2x + y)(2x + -1y))(x2 + 5y2) = 0


Subproblem 1
Set the factor '(x2 + 5y2)' equal to zero and attempt to solve:

Simplifying
x2 + 5y2 = 0

Solving
x2 + 5y2 = 0

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

Add '-5y2' to each side of the equation.
x2 + 5y2 + -5y2 = 0 + -5y2

Combine like terms: 5y2 + -5y2 = 0
x2 + 0 = 0 + -5y2
x2 = 0 + -5y2
Remove the zero:
x2 = -5y2

Simplifying
x2 = -5y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

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

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

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

Simplifying
x = -0.5y

Subproblem 3
Set the factor '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

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

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

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y
Solution
x = {-0.5y, 0.5y}

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