13a^2+5a-8=0

Solution for 13a^2+5a-8=0 equation:

Simplifying
13a2 + 5a + -8 = 0

Reorder the terms:
-8 + 5a + 13a2 = 0

Solving
-8 + 5a + 13a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -1a)(8 + -13a) = 0

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

Simplifying
-1 + -1a = 0

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

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

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

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

Simplifying
a = -1
Subproblem 2
Set the factor '(8 + -13a)' equal to zero and attempt to solve:

Simplifying
8 + -13a = 0

Solving
8 + -13a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -13a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -13a = 0 + -8
-13a = 0 + -8

Combine like terms: 0 + -8 = -8
-13a = -8

Divide each side by '-13'.
a = 0.6153846154

Simplifying
a = 0.6153846154
Solution
a = {-1, 0.6153846154}