0=6a+24-9a^2

Solution for 0=6a+24-9a^2 equation:

Simplifying
0 = 6a + 24 + -9a2

Reorder the terms:
0 = 24 + 6a + -9a2

Solving
0 = 24 + 6a + -9a2

Solving for variable 'a'.

Combine like terms: 0 + -24 = -24
-24 + -6a + 9a2 = 24 + 6a + -9a2 + -24 + -6a + 9a2

Reorder the terms:
-24 + -6a + 9a2 = 24 + -24 + 6a + -6a + -9a2 + 9a2

Combine like terms: 24 + -24 = 0
-24 + -6a + 9a2 = 0 + 6a + -6a + -9a2 + 9a2
-24 + -6a + 9a2 = 6a + -6a + -9a2 + 9a2

Combine like terms: 6a + -6a = 0
-24 + -6a + 9a2 = 0 + -9a2 + 9a2
-24 + -6a + 9a2 = -9a2 + 9a2

Combine like terms: -9a2 + 9a2 = 0
-24 + -6a + 9a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -2a + 3a2) = 0

Factor a trinomial.
3((-4 + -3a)(2 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -3a)' equal to zero and attempt to solve:

Simplifying
-4 + -3a = 0

Solving
-4 + -3a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3a = 0 + 4
-3a = 0 + 4

Combine like terms: 0 + 4 = 4
-3a = 4

Divide each side by '-3'.
a = -1.333333333

Simplifying
a = -1.333333333
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-1.333333333, 2}