5x^3(4x^2-1)=

Solution for 5x^3(4x^2-1)= equation:

Simplifying
5x3(4x2 + -1) = 0

Reorder the terms:
5x3(-1 + 4x2) = 0
(-1 * 5x3 + 4x2 * 5x3) = 0
(-5x3 + 20x5) = 0

Solving
-5x3 + 20x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x3'.
5x3(-1 + 4x2) = 0

Factor a difference between two squares.
5x3((1 + 2x)(-1 + 2x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

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

Simplifying
x = -0.5
Subproblem 3
Set the factor '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

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

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.5, 0.5}