a(a^4-3a^3+a^2)=0

Solution for a(a^4-3a^3+a^2)=0 equation:

Simplifying
a(a4 + -3a3 + a2) = 0

Reorder the terms:
a(a2 + -3a3 + a4) = 0
(a2 * a + -3a3 * a + a4 * a) = 0
(a3 + -3a4 + a5) = 0

Solving
a3 + -3a4 + a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a3'.
a3(1 + -3a + a2) = 0

Subproblem 1
Set the factor 'a3' equal to zero and attempt to solve:

Simplifying
a3 = 0

Solving
a3 = 0

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

Simplifying
a3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -3a + a2)' equal to zero and attempt to solve:

Simplifying
1 + -3a + a2 = 0

Solving
1 + -3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3a + -1 + a2 = 0 + -1

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

Combine like terms: 1 + -1 = 0
0 + -3a + a2 = 0 + -1
-3a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3a + a2 = -1

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 = -1 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3a + a2 = 1.25

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(a + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
a + -1.5 = 1.118033989

Simplifying
a + -1.5 = 1.118033989

Reorder the terms:
-1.5 + a = 1.118033989

Solving
-1.5 + a = 1.118033989

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = 1.118033989 + 1.5
a = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
a = 2.618033989

Simplifying
a = 2.618033989

Subproblem 2
a + -1.5 = -1.118033989

Simplifying
a + -1.5 = -1.118033989

Reorder the terms:
-1.5 + a = -1.118033989

Solving
-1.5 + a = -1.118033989

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = -1.118033989 + 1.5
a = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
a = 0.381966011

Simplifying
a = 0.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.618033989, 0.381966011}
Solution
a = {2.618033989, 0.381966011}