(3x^2-9y^6)*(3x^2-9y^6)=

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Solution for (3x^2-9y^6)*(3x^2-9y^6)= equation: 


Simplifying
(3x2 + -9y6)(3x2 + -9y6) = 0

Multiply (3x2 + -9y6) * (3x2 + -9y6)
(3x2 * (3x2 + -9y6) + -9y6 * (3x2 + -9y6)) = 0
((3x2 * 3x2 + -9y6 * 3x2) + -9y6 * (3x2 + -9y6)) = 0

Reorder the terms:
((-27x2y6 + 9x4) + -9y6 * (3x2 + -9y6)) = 0
((-27x2y6 + 9x4) + -9y6 * (3x2 + -9y6)) = 0
(-27x2y6 + 9x4 + (3x2 * -9y6 + -9y6 * -9y6)) = 0
(-27x2y6 + 9x4 + (-27x2y6 + 81y12)) = 0

Reorder the terms:
(-27x2y6 + -27x2y6 + 9x4 + 81y12) = 0

Combine like terms: -27x2y6 + -27x2y6 = -54x2y6
(-54x2y6 + 9x4 + 81y12) = 0

Solving
-54x2y6 + 9x4 + 81y12 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-6x2y6 + x4 + 9y12) = 0

Factor a trinomial.
9((x2 + -3y6)(x2 + -3y6)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(x2 + -3y6)' equal to zero and attempt to solve:

Simplifying
x2 + -3y6 = 0

Solving
x2 + -3y6 = 0

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

Add '3y6' to each side of the equation.
x2 + -3y6 + 3y6 = 0 + 3y6

Combine like terms: -3y6 + 3y6 = 0
x2 + 0 = 0 + 3y6
x2 = 0 + 3y6
Remove the zero:
x2 = 3y6

Simplifying
x2 = 3y6

Take the square root of each side:
x = {-1.732050808y3, 1.732050808y3}

Subproblem 2
Set the factor '(x2 + -3y6)' equal to zero and attempt to solve:

Simplifying
x2 + -3y6 = 0

Solving
x2 + -3y6 = 0

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

Add '3y6' to each side of the equation.
x2 + -3y6 + 3y6 = 0 + 3y6

Combine like terms: -3y6 + 3y6 = 0
x2 + 0 = 0 + 3y6
x2 = 0 + 3y6
Remove the zero:
x2 = 3y6

Simplifying
x2 = 3y6

Take the square root of each side:
x = {-1.732050808y3, 1.732050808y3}
Solution
x = {-1.732050808y3, 1.732050808y3, -1.732050808y3, 1.732050808y3}

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