(2x^2+1)(4x)=0

Solution for (2x^2+1)(4x)=0 equation:

Simplifying
(2x2 + 1)(4x) = 0

Reorder the terms:
(1 + 2x2)(4x) = 0

Remove parenthesis around (4x)
(1 + 2x2) * 4x = 0

Reorder the terms for easier multiplication:
4x(1 + 2x2) = 0
(1 * 4x + 2x2 * 4x) = 0
(4x + 8x3) = 0

Solving
4x + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(1 + 2x2) = 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 '(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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}