0=6a+9a^2

Solution for 0=6a+9a^2 equation:

Simplifying
0 = 6a + 9a2

Solving
0 = 6a + 9a2

Solving for variable 'a'.
Remove the zero:
-6a + -9a2 = 6a + 9a2 + -6a + -9a2

Reorder the terms:
-6a + -9a2 = 6a + -6a + 9a2 + -9a2

Combine like terms: 6a + -6a = 0
-6a + -9a2 = 0 + 9a2 + -9a2
-6a + -9a2 = 9a2 + -9a2

Combine like terms: 9a2 + -9a2 = 0
-6a + -9a2 = 0

Factor out the Greatest Common Factor (GCF), '-3a'.
-3a(2 + 3a) = 0

Ignore the factor -3.
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 '(2 + 3a)' equal to zero and attempt to solve:

Simplifying
2 + 3a = 0

Solving
2 + 3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a = 0 + -2
3a = 0 + -2

Combine like terms: 0 + -2 = -2
3a = -2

Divide each side by '3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Solution
a = {0, -0.6666666667}