4x^3+21x+x=0

Solution for 4x^3+21x+x=0 equation:

Simplifying
4x3 + 21x + x = 0

Reorder the terms:
21x + x + 4x3 = 0

Combine like terms: 21x + x = 22x
22x + 4x3 = 0

Solving
22x + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(11 + 2x2) = 0

Ignore the factor 2.
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 '(11 + 2x2)' equal to zero and attempt to solve:

Simplifying
11 + 2x2 = 0

Solving
11 + 2x2 = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2x2 = 0 + -11
2x2 = 0 + -11

Combine like terms: 0 + -11 = -11
2x2 = -11

Divide each side by '2'.
x2 = -5.5

Simplifying
x2 = -5.5

The solution to this equation could not be determined.

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