9a^2+9=-3a

Solution for 9a^2+9=-3a equation:

Simplifying
9a2 + 9 = -3a

Reorder the terms:
9 + 9a2 = -3a

Solving
9 + 9a2 = -3a

Solving for variable 'a'.

Reorder the terms:
9 + 3a + 9a2 = -3a + 3a

Combine like terms: -3a + 3a = 0
9 + 3a + 9a2 = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + a + 3a2)' equal to zero and attempt to solve:

Simplifying
3 + a + 3a2 = 0

Solving
3 + a + 3a2 = 0

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

Divide each side by '3'.
1 + 0.3333333333a + a2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.3333333333a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + 0.3333333333a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.3333333333a + a2 = 0 + -1
0.3333333333a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.3333333333a + 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.
0.3333333333a + 0.25 + a2 = -1 + 0.25

Reorder the terms:
0.25 + 0.3333333333a + a2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + 0.3333333333a + 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.

The solution to this equation could not be determined.