6a^2+11a-65=0

Solution for 6a^2+11a-65=0 equation:

Simplifying
6a2 + 11a + -65 = 0

Reorder the terms:
-65 + 11a + 6a2 = 0

Solving
-65 + 11a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-13 + -3a)(5 + -2a) = 0

Subproblem 1
Set the factor '(-13 + -3a)' equal to zero and attempt to solve:

Simplifying
-13 + -3a = 0

Solving
-13 + -3a = 0

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

Add '13' to each side of the equation.
-13 + 13 + -3a = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3a = 0 + 13
-3a = 0 + 13

Combine like terms: 0 + 13 = 13
-3a = 13

Divide each side by '-3'.
a = -4.333333333

Simplifying
a = -4.333333333
Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 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 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Solution
a = {-4.333333333, 2.5}