60a^2+33a-9=0

Solution for 60a^2+33a-9=0 equation:

Simplifying
60a2 + 33a + -9 = 0

Reorder the terms:
-9 + 33a + 60a2 = 0

Solving
-9 + 33a + 60a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 11a + 20a2) = 0

Factor a trinomial.
3((-3 + -4a)(1 + -5a)) = 0

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

Simplifying
-3 + -4a = 0

Solving
-3 + -4a = 0

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

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

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

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

Divide each side by '-4'.
a = -0.75

Simplifying
a = -0.75
Subproblem 2
Set the factor '(1 + -5a)' equal to zero and attempt to solve:

Simplifying
1 + -5a = 0

Solving
1 + -5a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5a = 0 + -1
-5a = 0 + -1

Combine like terms: 0 + -1 = -1
-5a = -1

Divide each side by '-5'.
a = 0.2

Simplifying
a = 0.2
Solution
a = {-0.75, 0.2}