(4x^2-8y^2)(x^2-7y^2)=

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Solution for (4x^2-8y^2)(x^2-7y^2)= equation: 


Simplifying
(4x2 + -8y2)(x2 + -7y2) = 0

Multiply (4x2 + -8y2) * (x2 + -7y2)
(4x2 * (x2 + -7y2) + -8y2 * (x2 + -7y2)) = 0
((x2 * 4x2 + -7y2 * 4x2) + -8y2 * (x2 + -7y2)) = 0

Reorder the terms:
((-28x2y2 + 4x4) + -8y2 * (x2 + -7y2)) = 0
((-28x2y2 + 4x4) + -8y2 * (x2 + -7y2)) = 0
(-28x2y2 + 4x4 + (x2 * -8y2 + -7y2 * -8y2)) = 0
(-28x2y2 + 4x4 + (-8x2y2 + 56y4)) = 0

Reorder the terms:
(-28x2y2 + -8x2y2 + 4x4 + 56y4) = 0

Combine like terms: -28x2y2 + -8x2y2 = -36x2y2
(-36x2y2 + 4x4 + 56y4) = 0

Solving
-36x2y2 + 4x4 + 56y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9x2y2 + x4 + 14y4) = 0

Factor a trinomial.
4((x2 + -7y2)(x2 + -2y2)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(x2 + -7y2)' equal to zero and attempt to solve:

Simplifying
x2 + -7y2 = 0

Solving
x2 + -7y2 = 0

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

Add '7y2' to each side of the equation.
x2 + -7y2 + 7y2 = 0 + 7y2

Combine like terms: -7y2 + 7y2 = 0
x2 + 0 = 0 + 7y2
x2 = 0 + 7y2
Remove the zero:
x2 = 7y2

Simplifying
x2 = 7y2

Take the square root of each side:
x = {-2.645751311y, 2.645751311y}

Subproblem 2
Set the factor '(x2 + -2y2)' equal to zero and attempt to solve:

Simplifying
x2 + -2y2 = 0

Solving
x2 + -2y2 = 0

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

Add '2y2' to each side of the equation.
x2 + -2y2 + 2y2 = 0 + 2y2

Combine like terms: -2y2 + 2y2 = 0
x2 + 0 = 0 + 2y2
x2 = 0 + 2y2
Remove the zero:
x2 = 2y2

Simplifying
x2 = 2y2

Take the square root of each side:
x = {-1.414213562y, 1.414213562y}
Solution
x = {-2.645751311y, 2.645751311y, -1.414213562y, 1.414213562y}

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