-a^3+3a^2-5a=

Solution for -a^3+3a^2-5a= equation:

Simplifying
-1a3 + 3a2 + -5a = 0

Reorder the terms:
-5a + 3a2 + -1a3 = 0

Solving
-5a + 3a2 + -1a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-5 + 3a + -1a2) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-5 + 3a + -1a2)' equal to zero and attempt to solve:

Simplifying
-5 + 3a + -1a2 = 0

Solving
-5 + 3a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -3a + a2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -3a + -5 + a2 = 0 + -5

Reorder the terms:
5 + -5 + -3a + a2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a + a2 = 0 + -5
-3a + a2 = 0 + -5

Combine like terms: 0 + -5 = -5
-3a + a2 = -5

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -5 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -5 + 2.25

Combine like terms: -5 + 2.25 = -2.75
2.25 + -3a + a2 = -2.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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