3a^2-13a-38=0

Solution for 3a^2-13a-38=0 equation:

Simplifying
3a2 + -13a + -38 = 0

Reorder the terms:
-38 + -13a + 3a2 = 0

Solving
-38 + -13a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -1a)(19 + -3a) = 0

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 '(19 + -3a)' equal to zero and attempt to solve:

Simplifying
19 + -3a = 0

Solving
19 + -3a = 0

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

Add '-19' to each side of the equation.
19 + -19 + -3a = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -3a = 0 + -19
-3a = 0 + -19

Combine like terms: 0 + -19 = -19
-3a = -19

Divide each side by '-3'.
a = 6.333333333

Simplifying
a = 6.333333333
Solution
a = {-2, 6.333333333}