Simplifying
25x^{3} + -10x^{2} + -3x = 0
Reorder the terms:
-3x + -10x^{2} + 25x^{3} = 0
Solving
-3x + -10x^{2} + 25x^{3} = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + -10x + 25x^{2}) = 0
Factor a trinomial.
x((-1 + -5x)(3 + -5x)) = 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 + -5x)' equal to zero and attempt to solve:
Simplifying
-1 + -5x = 0
Solving
-1 + -5x = 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 + -5x = 0 + 1
Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1
Combine like terms: 0 + 1 = 1
-5x = 1
Divide each side by '-5'.
x = -0.2
Simplifying
x = -0.2
#### Subproblem 3

Set the factor '(3 + -5x)' equal to zero and attempt to solve:
Simplifying
3 + -5x = 0
Solving
3 + -5x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + -5x = 0 + -3
Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3
Combine like terms: 0 + -3 = -3
-5x = -3
Divide each side by '-5'.
x = 0.6
Simplifying
x = 0.6#### Solution

x = {0, -0.2, 0.6}