=(x^2-3y^2)(x^2+7y^2)

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Solution for =(x^2-3y^2)(x^2+7y^2) equation: 


Simplifying
0 = (x2 + -3y2)(x2 + 7y2)

Multiply (x2 + -3y2) * (x2 + 7y2)
0 = (x2(x2 + 7y2) + -3y2 * (x2 + 7y2))
0 = ((x2 * x2 + 7y2 * x2) + -3y2 * (x2 + 7y2))

Reorder the terms:
0 = ((7x2y2 + x4) + -3y2 * (x2 + 7y2))
0 = ((7x2y2 + x4) + -3y2 * (x2 + 7y2))
0 = (7x2y2 + x4 + (x2 * -3y2 + 7y2 * -3y2))
0 = (7x2y2 + x4 + (-3x2y2 + -21y4))

Reorder the terms:
0 = (7x2y2 + -3x2y2 + x4 + -21y4)

Combine like terms: 7x2y2 + -3x2y2 = 4x2y2
0 = (4x2y2 + x4 + -21y4)

Solving
0 = 4x2y2 + x4 + -21y4

Solving for variable 'x'.
Remove the zero:
-4x2y2 + -1x4 + 21y4 = 4x2y2 + x4 + -21y4 + -4x2y2 + -1x4 + 21y4

Reorder the terms:
-4x2y2 + -1x4 + 21y4 = 4x2y2 + -4x2y2 + x4 + -1x4 + -21y4 + 21y4

Combine like terms: 4x2y2 + -4x2y2 = 0
-4x2y2 + -1x4 + 21y4 = 0 + x4 + -1x4 + -21y4 + 21y4
-4x2y2 + -1x4 + 21y4 = x4 + -1x4 + -21y4 + 21y4

Combine like terms: x4 + -1x4 = 0
-4x2y2 + -1x4 + 21y4 = 0 + -21y4 + 21y4
-4x2y2 + -1x4 + 21y4 = -21y4 + 21y4

Combine like terms: -21y4 + 21y4 = 0
-4x2y2 + -1x4 + 21y4 = 0

Factor a trinomial.
(-1x2 + -7y2)(x2 + -3y2) = 0


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

Simplifying
-1x2 + -7y2 = 0

Solving
-1x2 + -7y2 = 0

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

Add '7y2' to each side of the equation.
-1x2 + -7y2 + 7y2 = 0 + 7y2

Combine like terms: -7y2 + 7y2 = 0
-1x2 + 0 = 0 + 7y2
-1x2 = 0 + 7y2
Remove the zero:
-1x2 = 7y2

Divide each side by '-1'.
x2 = -7y2

Simplifying
x2 = -7y2

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 '(x2 + -3y2)' equal to zero and attempt to solve:

Simplifying
x2 + -3y2 = 0

Solving
x2 + -3y2 = 0

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

Add '3y2' to each side of the equation.
x2 + -3y2 + 3y2 = 0 + 3y2

Combine like terms: -3y2 + 3y2 = 0
x2 + 0 = 0 + 3y2
x2 = 0 + 3y2
Remove the zero:
x2 = 3y2

Simplifying
x2 = 3y2

Take the square root of each side:
x = {-1.732050808y, 1.732050808y}
Solution
x = {-1.732050808y, 1.732050808y}

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