0=9a^2-3a-30

Solution for 0=9a^2-3a-30 equation:

Simplifying
0 = 9a2 + -3a + -30

Reorder the terms:
0 = -30 + -3a + 9a2

Solving
0 = -30 + -3a + 9a2

Solving for variable 'a'.

Combine like terms: 0 + 30 = 30
30 + 3a + -9a2 = -30 + -3a + 9a2 + 30 + 3a + -9a2

Reorder the terms:
30 + 3a + -9a2 = -30 + 30 + -3a + 3a + 9a2 + -9a2

Combine like terms: -30 + 30 = 0
30 + 3a + -9a2 = 0 + -3a + 3a + 9a2 + -9a2
30 + 3a + -9a2 = -3a + 3a + 9a2 + -9a2

Combine like terms: -3a + 3a = 0
30 + 3a + -9a2 = 0 + 9a2 + -9a2
30 + 3a + -9a2 = 9a2 + -9a2

Combine like terms: 9a2 + -9a2 = 0
30 + 3a + -9a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + a + -3a2) = 0

Factor a trinomial.
3((2 + -1a)(5 + 3a)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + 3a)' equal to zero and attempt to solve:

Simplifying
5 + 3a = 0

Solving
5 + 3a = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3a = 0 + -5
3a = 0 + -5

Combine like terms: 0 + -5 = -5
3a = -5

Divide each side by '3'.
a = -1.666666667

Simplifying
a = -1.666666667
Solution
a = {2, -1.666666667}