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

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

Simplifying
(x3 + -2x)(4x2 + 3) = 0

Reorder the terms:
(-2x + x3)(4x2 + 3) = 0

Reorder the terms:
(-2x + x3)(3 + 4x2) = 0

Multiply (-2x + x3) * (3 + 4x2)
(-2x * (3 + 4x2) + x3(3 + 4x2)) = 0
((3 * -2x + 4x2 * -2x) + x3(3 + 4x2)) = 0
((-6x + -8x3) + x3(3 + 4x2)) = 0
(-6x + -8x3 + (3 * x3 + 4x2 * x3)) = 0
(-6x + -8x3 + (3x3 + 4x5)) = 0

Combine like terms: -8x3 + 3x3 = -5x3
(-6x + -5x3 + 4x5) = 0

Solving
-6x + -5x3 + 4x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + -5x2 + 4x4) = 0

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

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 '(-3 + -4x2)' equal to zero and attempt to solve:

Simplifying
-3 + -4x2 = 0

Solving
-3 + -4x2 = 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 + -4x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x2 = 0 + 3
-4x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4x2 = 3

Divide each side by '-4'.
x2 = -0.75

Simplifying
x2 = -0.75

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 '(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

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {0, -1.414213562, 1.414213562}