3a^2-7a-66=0

Solution for 3a^2-7a-66=0 equation:

Simplifying
3a2 + -7a + -66 = 0

Reorder the terms:
-66 + -7a + 3a2 = 0

Solving
-66 + -7a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-11 + -3a)(6 + -1a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-3.666666667, 6}