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

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

Simplifying
2a(a3 + a2 + a) + -1a(a3 + a2 + a) = 0

Reorder the terms:
2a(a + a2 + a3) + -1a(a3 + a2 + a) = 0
(a * 2a + a2 * 2a + a3 * 2a) + -1a(a3 + a2 + a) = 0
(2a2 + 2a3 + 2a4) + -1a(a3 + a2 + a) = 0

Reorder the terms:
2a2 + 2a3 + 2a4 + -1a(a + a2 + a3) = 0
2a2 + 2a3 + 2a4 + (a * -1a + a2 * -1a + a3 * -1a) = 0
2a2 + 2a3 + 2a4 + (-1a2 + -1a3 + -1a4) = 0

Reorder the terms:
2a2 + -1a2 + 2a3 + -1a3 + 2a4 + -1a4 = 0

Combine like terms: 2a2 + -1a2 = 1a2
1a2 + 2a3 + -1a3 + 2a4 + -1a4 = 0

Combine like terms: 2a3 + -1a3 = 1a3
1a2 + 1a3 + 2a4 + -1a4 = 0

Combine like terms: 2a4 + -1a4 = 1a4
1a2 + 1a3 + 1a4 = 0

Solving
1a2 + 1a3 + 1a4 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(1 + a + a2)' equal to zero and attempt to solve:

Simplifying
1 + a + a2 = 0

Solving
1 + a + a2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The a term is a.  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.
a + 0.25 + a2 = -1 + 0.25

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

Combine like terms: -1 + 0.25 = -0.75
0.25 + a + a2 = -0.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -0.75

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}