-8x^2-13x-5=0

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

Simplifying
-8x2 + -13x + -5 = 0

Reorder the terms:
-5 + -13x + -8x2 = 0

Solving
-5 + -13x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 13x + 8x2) = 0

Factor a trinomial.
-1((1 + x)(5 + 8x)) = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(5 + 8x)' equal to zero and attempt to solve:

Simplifying
5 + 8x = 0

Solving
5 + 8x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 8x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8x = 0 + -5
8x = 0 + -5

Combine like terms: 0 + -5 = -5
8x = -5

Divide each side by '8'.
x = -0.625

Simplifying
x = -0.625
Solution
x = {-1, -0.625}