Simplifying
2x^{3} + -9x^{2} + -5x = 0
Reorder the terms:
-5x + -9x^{2} + 2x^{3} = 0
Solving
-5x + -9x^{2} + 2x^{3} = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + -9x + 2x^{2}) = 0
Factor a trinomial.
x((-1 + -2x)(5 + -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 '(-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 '(5 + -1x)' equal to zero and attempt to solve:
Simplifying
5 + -1x = 0
Solving
5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5
Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5
Combine like terms: 0 + -5 = -5
-1x = -5
Divide each side by '-1'.
x = 5
Simplifying
x = 5#### Solution

x = {0, -0.5, 5}