(3x^2-3y^2)(x^2-5y^2)=

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Solution for (3x^2-3y^2)(x^2-5y^2)= equation: 


Simplifying
(3x2 + -3y2)(x2 + -5y2) = 0

Multiply (3x2 + -3y2) * (x2 + -5y2)
(3x2 * (x2 + -5y2) + -3y2 * (x2 + -5y2)) = 0
((x2 * 3x2 + -5y2 * 3x2) + -3y2 * (x2 + -5y2)) = 0

Reorder the terms:
((-15x2y2 + 3x4) + -3y2 * (x2 + -5y2)) = 0
((-15x2y2 + 3x4) + -3y2 * (x2 + -5y2)) = 0
(-15x2y2 + 3x4 + (x2 * -3y2 + -5y2 * -3y2)) = 0
(-15x2y2 + 3x4 + (-3x2y2 + 15y4)) = 0

Reorder the terms:
(-15x2y2 + -3x2y2 + 3x4 + 15y4) = 0

Combine like terms: -15x2y2 + -3x2y2 = -18x2y2
(-18x2y2 + 3x4 + 15y4) = 0

Solving
-18x2y2 + 3x4 + 15y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6x2y2 + x4 + 5y4) = 0

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

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

Ignore the factor 3.

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

Take the square root of each side:
x = {-2.236067978y, 2.236067978y}

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y
Solution
x = {-2.236067978y, 2.236067978y, -1y, y}

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