(x^2-3)*(4x^2-9)=0

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Solution for (x^2-3)*(4x^2-9)=0 equation: 


Simplifying
(x2 + -3)(4x2 + -9) = 0

Reorder the terms:
(-3 + x2)(4x2 + -9) = 0

Reorder the terms:
(-3 + x2)(-9 + 4x2) = 0

Multiply (-3 + x2) * (-9 + 4x2)
(-3(-9 + 4x2) + x2(-9 + 4x2)) = 0
((-9 * -3 + 4x2 * -3) + x2(-9 + 4x2)) = 0
((27 + -12x2) + x2(-9 + 4x2)) = 0
(27 + -12x2 + (-9 * x2 + 4x2 * x2)) = 0
(27 + -12x2 + (-9x2 + 4x4)) = 0

Combine like terms: -12x2 + -9x2 = -21x2
(27 + -21x2 + 4x4) = 0

Solving
27 + -21x2 + 4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -4x2)(3 + -1x2) = 0

Factor a difference between two squares.
((3 + 2x)(3 + -2x))(3 + -1x2) = 0


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

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

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

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.732050808, 1.732050808, -1.5, 1.5}

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