(4x^2-2)(2x^2+3)=0

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

Simplifying
(4x2 + -2)(2x2 + 3) = 0

Reorder the terms:
(-2 + 4x2)(2x2 + 3) = 0

Reorder the terms:
(-2 + 4x2)(3 + 2x2) = 0

Multiply (-2 + 4x2) * (3 + 2x2)
(-2(3 + 2x2) + 4x2 * (3 + 2x2)) = 0
((3 * -2 + 2x2 * -2) + 4x2 * (3 + 2x2)) = 0
((-6 + -4x2) + 4x2 * (3 + 2x2)) = 0
(-6 + -4x2 + (3 * 4x2 + 2x2 * 4x2)) = 0
(-6 + -4x2 + (12x2 + 8x4)) = 0

Combine like terms: -4x2 + 12x2 = 8x2
(-6 + 8x2 + 8x4) = 0

Solving
-6 + 8x2 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4x2 + 4x4) = 0

Factor a trinomial.
2((-3 + -2x2)(1 + -2x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -2x2)' equal to zero and attempt to solve:

Simplifying
-3 + -2x2 = 0

Solving
-3 + -2x2 = 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 + -2x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x2 = 0 + 3
-2x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2x2 = 3

Divide each side by '-2'.
x2 = -1.5

Simplifying
x2 = -1.5

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 '(1 + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 = 0 + -1
-2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 = -1

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Solution
x = {-0.707106781, 0.707106781}