6ax^2+6ax+6a=0

Solution for 6ax^2+6ax+6a=0 equation:

Simplifying
6ax2 + 6ax + 6a = 0

Reorder the terms:
6a + 6ax + 6ax2 = 0

Solving
6a + 6ax + 6ax2 = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), '6a'.
6a(1 + x + x2) = 0

Ignore the factor 6.
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 '(1 + x + x2)' equal to zero and attempt to solve:

Simplifying
1 + x + x2 = 0

Solving
1 + x + x2 = 0

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

Add '-1' to each side of the equation.
1 + x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x + x2 = 0 + -1
x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x + x2 = -1

Add '-1x' to each side of the equation.
x + -1x + x2 = -1 + -1x

Combine like terms: x + -1x = 0
0 + x2 = -1 + -1x
x2 = -1 + -1x

Add '-1x2' to each side of the equation.
x2 + -1x2 = -1 + -1x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -1 + -1x + -1x2

Simplifying
0 = -1 + -1x + -1x2

The solution to this equation could not be determined.

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