a(6a^2+2a+9)=

Solution for a(6a^2+2a+9)= equation:

Simplifying
a(6a2 + 2a + 9) = 0

Reorder the terms:
a(9 + 2a + 6a2) = 0
(9 * a + 2a * a + 6a2 * a) = 0
(9a + 2a2 + 6a3) = 0

Solving
9a + 2a2 + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(9 + 2a + 6a2) = 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 '(9 + 2a + 6a2)' equal to zero and attempt to solve:

Simplifying
9 + 2a + 6a2 = 0

Solving
9 + 2a + 6a2 = 0

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

Divide each side by '6'.
1.5 + 0.3333333333a + a2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.3333333333a + -1.5 + a2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.3333333333a + a2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.3333333333a + a2 = 0 + -1.5
0.3333333333a + a2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.3333333333a + a2 = -1.5

The a term is 0.3333333333a.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333a + 0.02777777779 + a2 = -1.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333a + a2 = -1.5 + 0.02777777779

Combine like terms: -1.5 + 0.02777777779 = -1.47222222221
0.02777777779 + 0.3333333333a + a2 = -1.47222222221

Factor a perfect square on the left side:
(a + 0.1666666667)(a + 0.1666666667) = -1.47222222221

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}