(4x^3+8x)(x^2-3)=0

Solution for (4x^3+8x)(x^2-3)=0 equation:

Simplifying
(4x3 + 8x)(x2 + -3) = 0

Reorder the terms:
(8x + 4x3)(x2 + -3) = 0

Reorder the terms:
(8x + 4x3)(-3 + x2) = 0

Multiply (8x + 4x3) * (-3 + x2)
(8x * (-3 + x2) + 4x3 * (-3 + x2)) = 0
((-3 * 8x + x2 * 8x) + 4x3 * (-3 + x2)) = 0
((-24x + 8x3) + 4x3 * (-3 + x2)) = 0
(-24x + 8x3 + (-3 * 4x3 + x2 * 4x3)) = 0
(-24x + 8x3 + (-12x3 + 4x5)) = 0

Combine like terms: 8x3 + -12x3 = -4x3
(-24x + -4x3 + 4x5) = 0

Solving
-24x + -4x3 + 4x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-6 + -1x2 + x4) = 0

Factor a trinomial.
4x((-2 + -1x2)(3 + -1x2)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-2 + -1x2)' equal to zero and attempt to solve:

Simplifying
-2 + -1x2 = 0

Solving
-2 + -1x2 = 0

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

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

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

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

Divide each side by '-1'.
x2 = -2

Simplifying
x2 = -2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
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}
Solution
x = {0, -1.732050808, 1.732050808}