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}