3a^2-2a-33=0

Solution for 3a^2-2a-33=0 equation:

Simplifying
3a2 + -2a + -33 = 0

Reorder the terms:
-33 + -2a + 3a2 = 0

Solving
-33 + -2a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a)(11 + -3a) = 0

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

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 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 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(11 + -3a)' equal to zero and attempt to solve:

Simplifying
11 + -3a = 0

Solving
11 + -3a = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3a = 0 + -11
-3a = 0 + -11

Combine like terms: 0 + -11 = -11
-3a = -11

Divide each side by '-3'.
a = 3.666666667

Simplifying
a = 3.666666667
Solution
a = {-3, 3.666666667}