(3x^2-8y^2)(x^2-6y^2)=

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Solution for (3x^2-8y^2)(x^2-6y^2)= equation: 


Simplifying
(3x2 + -8y2)(x2 + -6y2) = 0

Multiply (3x2 + -8y2) * (x2 + -6y2)
(3x2 * (x2 + -6y2) + -8y2 * (x2 + -6y2)) = 0
((x2 * 3x2 + -6y2 * 3x2) + -8y2 * (x2 + -6y2)) = 0

Reorder the terms:
((-18x2y2 + 3x4) + -8y2 * (x2 + -6y2)) = 0
((-18x2y2 + 3x4) + -8y2 * (x2 + -6y2)) = 0
(-18x2y2 + 3x4 + (x2 * -8y2 + -6y2 * -8y2)) = 0
(-18x2y2 + 3x4 + (-8x2y2 + 48y4)) = 0

Reorder the terms:
(-18x2y2 + -8x2y2 + 3x4 + 48y4) = 0

Combine like terms: -18x2y2 + -8x2y2 = -26x2y2
(-26x2y2 + 3x4 + 48y4) = 0

Solving
-26x2y2 + 3x4 + 48y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x2 + -6y2)(3x2 + -8y2) = 0


Subproblem 1
Set the factor '(x2 + -6y2)' equal to zero and attempt to solve:

Simplifying
x2 + -6y2 = 0

Solving
x2 + -6y2 = 0

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

Add '6y2' to each side of the equation.
x2 + -6y2 + 6y2 = 0 + 6y2

Combine like terms: -6y2 + 6y2 = 0
x2 + 0 = 0 + 6y2
x2 = 0 + 6y2
Remove the zero:
x2 = 6y2

Simplifying
x2 = 6y2

Take the square root of each side:
x = {-2.449489743y, 2.449489743y}

Subproblem 2
Set the factor '(3x2 + -8y2)' equal to zero and attempt to solve:

Simplifying
3x2 + -8y2 = 0

Solving
3x2 + -8y2 = 0

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

Add '8y2' to each side of the equation.
3x2 + -8y2 + 8y2 = 0 + 8y2

Combine like terms: -8y2 + 8y2 = 0
3x2 + 0 = 0 + 8y2
3x2 = 0 + 8y2
Remove the zero:
3x2 = 8y2

Divide each side by '3'.
x2 = 2.666666667y2

Simplifying
x2 = 2.666666667y2

Take the square root of each side:
x = {-1.632993162y, 1.632993162y}
Solution
x = {-2.449489743y, 2.449489743y, -1.632993162y, 1.632993162y}

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