Simplifying
x^{3} + 3x^{2} + -4x = 0
Reorder the terms:
-4x + 3x^{2} + x^{3} = 0
Solving
-4x + 3x^{2} + x^{3} = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 3x + x^{2}) = 0
Factor a trinomial.
x((-4 + -1x)(1 + -1x)) = 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 '(-4 + -1x)' equal to zero and attempt to solve:
Simplifying
-4 + -1x = 0
Solving
-4 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4
Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4
Combine like terms: 0 + 4 = 4
-1x = 4
Divide each side by '-1'.
x = -4
Simplifying
x = -4
#### Subproblem 3

Set the factor '(1 + -1x)' equal to zero and attempt to solve:
Simplifying
1 + -1x = 0
Solving
1 + -1x = 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 + -1x = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1
Combine like terms: 0 + -1 = -1
-1x = -1
Divide each side by '-1'.
x = 1
Simplifying
x = 1#### Solution

x = {0, -4, 1}