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

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

Simplifying
a3 + -1a2 + 4a = 0

Reorder the terms:
4a + -1a2 + a3 = 0

Solving
4a + -1a2 + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(4 + -1a + a2) = 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 '(4 + -1a + a2)' equal to zero and attempt to solve:

Simplifying
4 + -1a + a2 = 0

Solving
4 + -1a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -1a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + -1a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a + a2 = 0 + -4
-1a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
-1a + a2 = -4

The a term is -1a.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = -4 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + -1a + a2 = -3.75

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = -3.75

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}